Analysis of the Rosenblatt process
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 230-257.

We analyze the Rosenblatt process which is a selfsimilar process with stationary increments and which appears as limit in the so-called Non Central Limit Theorem (Dobrushin and Majòr (1979), Taqqu (1979)). This process is non-gaussian and it lives in the second Wiener chaos. We give its representation as a Wiener-Itô multiple integral with respect to the brownian motion on a finite interval and we develop a stochastic calculus with respect to it by using both pathwise type calculus and Malliavin calculus.

DOI : 10.1051/ps:2007037
Classification : 60G12, 60G15, 60H05, 60H07
Mots-clés : non central limit theorem, Rosenblatt process, fractional brownian motion, stochastic calculus via regularization, Malliavin calculus, Skorohod integral 
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     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps:2007037/}
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Tudor, Ciprian A. Analysis of the Rosenblatt process. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 230-257. doi : 10.1051/ps:2007037. https://www.numdam.org/articles/10.1051/ps:2007037/

[1] P. Abry and V. Pipiras, Wavelet-based synthesis of the Rosenblatt process. Signal Process. 86 (2006) 2326-2339. | Zbl

[2] J.M.P. Albin, A note on the Rosenblatt distributions. Statist. Probab. Lett. 40 (1998) 83-91. | MR | Zbl

[3] J.M.P. Albin, On extremal theory for self similar processes. Ann. Probab. 26 (1998) 743-793. | MR | Zbl

[4] E. Alòs, O. Mazet and D. Nualart, Stochastic calculus with respect to Gaussian processes. Ann. Probab. 29 (2001) 766-801. | MR | Zbl

[5] E. Alòs and D. Nualart, Stochastic integration with respect to the fractional Brownian motion. Stoch. Stoch. Rep. 75 (2003) 129-152. | MR | Zbl

[6] T. Androshuk and Y. Mishura, Mixed Brownian-fractional Brownian model: absence of arbitrage and related topics. Stochastics An Int. J. Probability Stochastic Processes 78 (2006) 281-300. | MR | Zbl

[7] F. Biagini, M. Campanino and S. Fuschini, Discrete approximation of stochastic integrals with respect of fractional Brownian motion of Hurst index H>1/2. Preprint University of Bologna (2005). | MR | Zbl

[8] P. Cheridito, H. Kawaguchi and M. Maejima, Fractional Ornstein-Uhlenbeck processes. Electron. J. Probab. 8 (2003) 1-14. | EuDML | MR | Zbl

[9] L. Decreusefond and A.S. Ustunel, Stochastic analysis of the fractional Brownian motion. Potential Anal. 10 (1998) 177-214. | MR | Zbl

[10] G. Da Prato and J. Zabczyk, Stochastic equations in infinite dimensions. Cambridge University Press (1992). | MR | Zbl

[11] R.L. Dobrushin and P. Major, Non-central limit theorems for non-linear functionals of Gaussian fields. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50 (1979) 27-52. | MR | Zbl

[12] A. Drewitz, Mild solutions to stochastic evolution equations with fractional Brownian motion. Diploma thesis at TU Darmstadt (2005).

[13] P. Embrechts and M. Maejima, Selfsimilar processes. Princeton University Press, Princeton, New York (2002). | MR | Zbl

[14] R. Fox and M.S. Taqqu, Multiple stochastic integrals with dependent integrators. J. Mult. Anal. 21 (1987) 105-127. | MR | Zbl

[15] V. Goodman and J. Kuelbs, Gaussian chaos and functional law of the ierated logarithm for Itô-Wiener integrals. Ann. I.H.P., Section B 29 (1993) 485-512. | Numdam | MR | Zbl

[16] M. Gradinaru, I. Nourdin, F. Russo and P. Vallois, m-order integrals and generalized Itôs formula; the case of a fractional Brownian motion with any Hurst parameter. Preprint, to appear in Annales de l'Institut Henri Poincaré (2003). | Numdam | Zbl

[17] M. Gradinaru, I. Nourdin and S. Tindel, Ito's and Tanaka's type formulae for the stochastic heat equation. J. Funct. Anal. 228 (2005) 114-143. | MR | Zbl

[18] P. Hall, W. Hardle, T. Kleinow and P. Schmidt, Semiparametric Bootstrap Approach to Hypothesis tests and Confidence intervals for the Hurst coefficient. Stat. Infer. Stoch. Process. 3 (2000) 263-276. | MR | Zbl

[19] M. Jolis and M. Sanz, Integrator properties of the Skorohod integral. Stochastics and Stochastics Reports 41 (1992) 163-176. | MR | Zbl

[20] O. Kallenberg, On an independence criterion for multiple Wiener integrals. Ann. Probab. 19 (1991) 483-485. | MR | Zbl

[21] H. Kettani and J. Gubner, Estimation of the long-range dependence parameter of fractional Brownian motionin, in Proc. 28th IEEE LCN03 (2003).

[22] I. Kruk, F. Russo and C.A. Tudor, Wiener integrals, Malliavin calculus and covariance measure structure. J. Funct. Anal. 249 (2007) 92-142. | MR | Zbl

[23] N.N. Leonenko and V.V. Ahn, Rate of convergence to the Rosenblatt distribution for additive functionals of stochastic processes with long-range dependence. J. Appl. Math. Stoch. Anal. 14 (2001) 27-46. | MR | Zbl

[24] N.N. Leonenko and W. Woyczynski, Scaling limits of solutions of the heat equation for singular Non-Gaussian data. J. Stat. Phys. 91 423-438. | MR | Zbl

[25] M. Maejima and C.A. Tudor, Wiener integrals with respect to the Hermite process and a non central limit theorem. Stoch. Anal. Appl. 25 (2007) 1043-1056. | MR | Zbl

[26] O. Mocioalca and F. Viens, Skorohod integration and stochastic calculus beyond the fractional Brownian scale. J. Funct. Anal. 222 (2004) 385-434. | MR | Zbl

[27] I. Norros, E. Valkeila and J. Virtamo, An elementary approach to a Girsanov formula and other analytical results for fractional Brownian motion. Bernoulli 5 (1999) 571-587. | MR | Zbl

[28] I. Nourdin, A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one. Séminaire de Probabilités XLI (2006). To appear. | MR | Zbl

[29] D. Nualart, Malliavin Calculus and Related Topics. Springer (1995). | MR | Zbl

[30] D. Nualart and M. Zakai, Generalized mulptiple stochastic integrals and the representation of Wiener functionals. Stochastics 23 (1987) 311-330. | MR | Zbl

[31] V. Pipiras, Wavelet type expansion of the Rosenblatt process. J. Fourier Anal. Appl. 10 (2004) 599-634. | MR | Zbl

[32] V. Pipiras and M. Taqqu, Convergence of weighted sums of random variables with long range dependence. Stoch. Process. Appl. 90 (2000) 157-174. | MR | Zbl

[33] V. Pipiras and Murad Taqqu, Integration questions related to the fractional Brownian motion. Probab. Theor. Relat. Fields 118 (2001) 251-281. | MR | Zbl

[34] N. Privault and C.A. Tudor, Skorohod and pathwise stochastic calculus with respect to an L2-process. Rand. Oper. Stoch. Equ. 8 (2000) 201-204. | Zbl

[35] Z. Qian and T. Lyons, System control and rough paths. Clarendon Press, Oxford (2002). | MR | Zbl

[36] M. Rosenblatt, Independence and dependence. Proc. 4th Berkeley Symposium on Math, Stat. II (1961) 431-443. | MR | Zbl

[37] F. Russo and P. Vallois, Forward backward and symmetric stochastic integration. Probab. Theor. Relat. Fields 97 (1993) 403-421. | MR | Zbl

[38] F. Russo and P. Vallois, Stochastic calculus with respect to a finite quadratic variation process. Stoch. Stoch. Rep. 70 (2000) 1-40. | MR | Zbl

[39] F. Russo and P. Vallois, Elements of stochastic calculus via regularization. Preprint, to appear in Séminaire de Probabilités (2006). | MR | Zbl

[40] G. Samorodnitsky and M. Taqqu, Stable Non-Gaussian random variables. Chapman and Hall, London (1994). | MR

[41] A.S. Üstunel and M. Zakai, On independence and conditioning on Wiener space. Ann. Probab. 17 (1989) 1441-1453. | MR | Zbl

[42] M. Taqqu, Weak convergence to the fractional Brownian motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie verw. Gebiete 31 (1975) 287-302. | MR | Zbl

[43] M. Taqqu, Convergence of integrated processes of arbitrary Hermite rank. Z. Wahrscheinlichkeitstheorie verw. Gebiete 50 (1979) 53-83. | MR | Zbl

[44] M. Taqqu, A bibliographical guide to selfsimilar processes and long-range dependence. Dependence in Probability and Statistics, Birkhauser, Boston (1986) 137-162. | MR | Zbl

[45] S. Tindel, C.A. Tudor and F. Viens, Stochastic evolution equations with fractional Brownian motion. Probab. Theor. Relat. Fields. 127 (2003) 186-204. | MR | Zbl

[46] C.A. Tudor, Itô's formula for the infinite-dimensional fractional Brownian motion. J. Math. Kyoto University 45 (2005) 531-546. | MR | Zbl

[47] W.B. Wu, Unit root testing for functionals of linear processes. Econ. Theory 22 (2005) 1-14. | MR | Zbl

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  • Duncan, Tyrone E.; Pasik-Duncan, Bozenna, 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT) (2024), p. 1475 | DOI:10.1109/codit62066.2024.10708566
  • Duncan, Tyrone E.; Pasik-Duncan, Bozenna; Tembine, Hamidou, 2024 10th International Conference on Control, Decision and Information Technologies (CoDIT) (2024), p. 982 | DOI:10.1109/codit62066.2024.10708394
  • Duncan, Tyrone E.; Pasik-Duncan, Bozenna; Tembine, Hamidou, 2024 IEEE 63rd Conference on Decision and Control (CDC) (2024), p. 1850 | DOI:10.1109/cdc56724.2024.10886161
  • Čoupek, Petr; Kříž, Pavel; Maslowski, Bohdan, 2024 IEEE 63rd Conference on Decision and Control (CDC) (2024), p. 4227 | DOI:10.1109/cdc56724.2024.10886859
  • Mshary, Noorah; Ahmed, Hamdy M.; Ghanem, Ahmed S. Existence and controllability of nonlinear evolution equation involving Hilfer fractional derivative with noise and impulsive effect via Rosenblatt process and Poisson jumps, AIMS Mathematics, Volume 9 (2024) no. 4, p. 9746 | DOI:10.3934/math.2024477
  • Pasik-Duncan, Bozenna; E. Duncan, Tyrone On Advances in Noise Modeling in Stochastic Systems, Control and Adaptive Control, Adaptive Control Theory and Applications (2024) | DOI:10.5772/intechopen.1005451
  • Yan, Zuomao Approximate Optimal Control of Fractional Impulsive Partial Stochastic Differential Inclusions Driven by Rosenblatt Process, Applied Mathematics Optimization, Volume 89 (2024) no. 1 | DOI:10.1007/s00245-023-10071-9
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  • Yadav, Vandana; Vats, Ramesh Kumar; Kumar, Ankit New exploration on the existence and null controllability of fractional Hilfer stochastic systems driven by Poisson jumps and fractional Brownian motion with non-instantaneous impulse, International Journal of Dynamics and Control, Volume 12 (2024) no. 10, p. 3791 | DOI:10.1007/s40435-024-01451-2
  • Dhayal, Rajesh; Gómez-Aguilar, J. F.; Pérez-Careta, Eduardo Stability and controllability of ψ-Caputo fractional stochastic differential systems driven by Rosenblatt process with impulses, International Journal of Dynamics and Control, Volume 12 (2024) no. 5, p. 1626 | DOI:10.1007/s40435-023-01286-3
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  • Alnafisah, Yousef; Ahmed, Hamdy M. Null controllability of Hilfer fractional stochastic integrodifferential equations with noninstantaneous impulsive and Poisson jump, International Journal of Nonlinear Sciences and Numerical Simulation, Volume 24 (2023) no. 6, p. 2347 | DOI:10.1515/ijnsns-2020-0292
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  • Daw, Lara; Kerchev, George Fractal dimensions of the Rosenblatt process, Stochastic Processes and their Applications, Volume 161 (2023), p. 544 | DOI:10.1016/j.spa.2023.04.001
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  • Upadhyay, Anjali; Kumar, Surendra Existence of solutions for non-autonomous second-order stochastic inclusions with Clarke’s subdifferential and non instantaneous impulses, Filomat, Volume 36 (2022) no. 4, p. 1215 | DOI:10.2298/fil2204215u
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  • Almarri, Barakah; Elshenhab, Ahmed M. Controllability of Fractional Stochastic Delay Systems Driven by the Rosenblatt Process, Fractal and Fractional, Volume 6 (2022) no. 11, p. 664 | DOI:10.3390/fractalfract6110664
  • References, General Stochastic Measures (2022), p. 231 | DOI:10.1002/9781394163939.refs
  • Ahmed, Hamdy M. Hilfer fractional neutral stochastic partial differential equations with delay driven by Rosenblatt process, Journal of Control and Decision, Volume 9 (2022) no. 2, p. 226 | DOI:10.1080/23307706.2021.1953412
  • Čoupek, Petr; Maslowski, Bohdan; Ondreját, Martin Stochastic integration with respect to fractional processes in Banach spaces, Journal of Functional Analysis, Volume 282 (2022) no. 8, p. 109393 | DOI:10.1016/j.jfa.2022.109393
  • Kumar, Vivek; Mohan, Manil T.; Kumar Giri, Ankik On a generalized stochastic Burgers' equation perturbed by Volterra noise, Journal of Mathematical Analysis and Applications, Volume 506 (2022) no. 1, p. 125638 | DOI:10.1016/j.jmaa.2021.125638
  • Sun, Xichao; Yan, Litan; Ge, Yong The Laws of Large Numbers Associated with the Linear Self-attracting Diffusion Driven by Fractional Brownian Motion and Applications, Journal of Theoretical Probability, Volume 35 (2022) no. 3, p. 1423 | DOI:10.1007/s10959-021-01126-0
  • Duncan, Tyrone E.; Pasik-Duncan, Bozenna Advances in Noise Modeling for Stochastic Systems in Optimal Control, La Matematica, Volume 1 (2022) no. 3, p. 685 | DOI:10.1007/s44007-022-00025-y
  • Anukiruthika, K.; Muthukumar, P. Optimal Mild Solutions of Time-Fractional Stochastic Navier-Stokes Equation with Rosenblatt Process in Hilbert Space, Mathematical Modeling, Computational Intelligence Techniques and Renewable Energy, Volume 1405 (2022), p. 93 | DOI:10.1007/978-981-16-5952-2_9
  • Almarri, Barakah; Wang, Xingtao; Elshenhab, Ahmed M. Controllability of Stochastic Delay Systems Driven by the Rosenblatt Process, Mathematics, Volume 10 (2022) no. 22, p. 4223 | DOI:10.3390/math10224223
  • Dhayal, Rajesh; Francisco Gómez‐Aguilar, José; Fernández‐Anaya, Guillermo Optimal controls for fractional stochastic differential systems driven by Rosenblatt process with impulses, Optimal Control Applications and Methods, Volume 43 (2022) no. 2, p. 386 | DOI:10.1002/oca.2805
  • Kuehn, Christian; Lux, Kerstin; Neamţu, Alexandra Warning signs for non-Markovian bifurcations: colour blindness and scaling laws, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Volume 478 (2022) no. 2259 | DOI:10.1098/rspa.2021.0740
  • Ahmed, Hamdy M. Noninstantaneous Impulsive Conformable Fractional Stochastic Delay Integro-Differential System with Rosenblatt Process and Control Function, Qualitative Theory of Dynamical Systems, Volume 21 (2022) no. 1 | DOI:10.1007/s12346-021-00544-z
  • Chalishajar, Dimplekumar; Kasinathan, Ravikumar; Kasinathan, Ramkumar; Diop, Mamadou Abdoul Optimal control for neutral stochastic systems with infinite time delay and deviated argument driven by Rosenblatt process, Results in Control and Optimization, Volume 9 (2022), p. 100181 | DOI:10.1016/j.rico.2022.100181
  • Chalishajar, Dimplekumar Navinchandra; Kasinathan, Ravikumar; Kasinathan, Ramkumar; Diop, Mamadou Abdoul Optimal Controls for Neutral Stochastic Integrodifferential Equations with Infinite Time Delay and Deviated Argument Driven by Rosenblatt Process, SSRN Electronic Journal (2022) | DOI:10.2139/ssrn.4150578
  • Yu, Qian; Shen, Guangjun; Yin, Xiuwei Existence and Hölder continuity conditions for self-intersection local time of Rosenblatt process, Stochastic Analysis and Applications, Volume 40 (2022) no. 6, p. 978 | DOI:10.1080/07362994.2021.1973497
  • Russo, Francesco; Vallois, Pierre Examples of Finite Quadratic Variation Processes, Stochastic Calculus via Regularizations, Volume 11 (2022), p. 259 | DOI:10.1007/978-3-031-09446-0_8
  • Čoupek, Petr; Duncan, Tyrone E.; Pasik-Duncan, Bozenna A stochastic calculus for Rosenblatt processes, Stochastic Processes and their Applications, Volume 150 (2022), p. 853 | DOI:10.1016/j.spa.2020.01.004
  • Douissi, Soukaina; Es-Sebaiy, Khalifa; Alshahrani, Fatimah; Viens, Frederi G. AR(1) processes driven by second-chaos white noise: Berry–Esséen bounds for quadratic variation and parameter estimation, Stochastic Processes and their Applications, Volume 150 (2022), p. 886 | DOI:10.1016/j.spa.2020.02.007
  • Li, Xue-Mei; Sieber, Julian Mild stochastic sewing lemma, SPDE in random environment, and fractional averaging, Stochastics and Dynamics, Volume 22 (2022) no. 07 | DOI:10.1142/s0219493722400251
  • Dhayal, Rajesh; Malik, Muslim Approximate controllability of fractional stochastic differential equations driven by Rosenblatt process with non-instantaneous impulses, Chaos, Solitons Fractals, Volume 151 (2021), p. 111292 | DOI:10.1016/j.chaos.2021.111292
  • Araya, Héctor; Garzón, Johanna; Roa, Tania Non symmetric Rosenblatt process over a compact, Communications in Statistics - Theory and Methods, Volume 50 (2021) no. 23, p. 5517 | DOI:10.1080/03610926.2020.1734830
  • Dhayal, Rajesh; Malik, Muslim Existence and controllability of impulsive fractional stochastic differential equations driven by Rosenblatt process with Poisson jumps, Journal of Engineering Mathematics, Volume 130 (2021) no. 1 | DOI:10.1007/s10665-021-10167-7
  • Sathiyaraj, T.; Wang, JinRong; O'Regan, D. Controllability of stochastic nonlinear oscillating delay systems driven by the Rosenblatt distribution, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 151 (2021) no. 1, p. 217 | DOI:10.1017/prm.2020.11
  • Benkabdi, Youssef; Lakhel, E. Controllability of impulsive neutral stochastic integro-differential systems driven by a Rosenblatt process with unbounded delay, Random Operators and Stochastic Equations, Volume 29 (2021) no. 4, p. 237 | DOI:10.1515/rose-2021-2063
  • Ramkumar, K.; Ravikumar, K.; Varshini, S. Fractional neutral stochastic differential equations with Caputo fractional derivative: Fractional Brownian motion, Poisson jumps, and optimal control, Stochastic Analysis and Applications, Volume 39 (2021) no. 1, p. 157 | DOI:10.1080/07362994.2020.1789476
  • Ahmed, Hamdy M. Conformable fractional stochastic differential equations with control function, Systems Control Letters, Volume 158 (2021), p. 105062 | DOI:10.1016/j.sysconle.2021.105062
  • Duncan, Tyrone E.; Pasik-Duncan, Bozenna, 2020 59th IEEE Conference on Decision and Control (CDC) (2020), p. 343 | DOI:10.1109/cdc42340.2020.9304316
  • Shen, Guangjun; Sakthivel, R.; Ren, Yong; Li, Mengyu Controllability and stability of fractional stochastic functional systems driven by Rosenblatt process, Collectanea Mathematica, Volume 71 (2020) no. 1, p. 63 | DOI:10.1007/s13348-019-00248-3
  • Duncan, Tyrone E.; Pasik-Duncan, Bozenna Ergodic Linear-Quadratic Control for a Two Dimensional Stochastic System Driven by a Continuous Non-Gaussian Noise, IFAC-PapersOnLine, Volume 53 (2020) no. 2, p. 2177 | DOI:10.1016/j.ifacol.2020.12.2548
  • Saravanakumar, Subramaniam; Balasubramaniam, Pagavathigounder Approximate controllability of nonlinear Hilfer fractional stochastic differential system with Rosenblatt process and Poisson jumps, International Journal of Nonlinear Sciences and Numerical Simulation, Volume 21 (2020) no. 7-8, p. 727 | DOI:10.1515/ijnsns-2019-0141
  • Bai, Shuyang Representations of hermite processes using local time of intersecting stationary stable regenerative sets, Journal of Applied Probability, Volume 57 (2020) no. 4, p. 1234 | DOI:10.1017/jpr.2020.57
  • Kasinathan, Ravikumar; Kasinathan, Ramkumar; Hamit, Mahamat Hassan Mahamat; Diop, Mamadou Abdoul Exponential behavior of neutral impulsive stochastic integro-differential equations driven by Poisson jumps and Rosenblatt process, Nonautonomous Dynamical Systems, Volume 7 (2020) no. 1, p. 1 | DOI:10.1515/msds-2020-0001
  • Shevchenko, Radomyra; Tudor, Ciprian A. Parameter estimation for the Rosenblatt Ornstein–Uhlenbeck process with periodic mean, Statistical Inference for Stochastic Processes, Volume 23 (2020) no. 1, p. 227 | DOI:10.1007/s11203-019-09200-5
  • Lakhel, El Hassan; McKibben, M. A. Controllability for Time-dependent Neutral Stochastic Functional Differential Equations with Rosenblatt Process and Impulses, International Journal of Control, Automation and Systems, Volume 17 (2019) no. 2, p. 286 | DOI:10.1007/s12555-016-0363-5
  • STOYANOV, STOYAN V.; RACHEV, SVETLOZAR T.; MITTNIK, STEFAN; FABOZZI, FRANK J. PRICING DERIVATIVES IN HERMITE MARKETS, International Journal of Theoretical and Applied Finance, Volume 22 (2019) no. 06, p. 1950031 | DOI:10.1142/s0219024919500316
  • El Hassan, Lakhel Neutral stochastic functional differential evolution equations driven by Rosenblatt process with varying-time delays, Proyecciones (Antofagasta), Volume 38 (2019) no. 4, p. 665 | DOI:10.22199/issn.0717-6279-2019-04-0043
  • Lakhel, El Hassan; Tlidi, Abdelmonaim Existence, uniqueness and stability of impulsive stochastic neutral functional differential equations driven by Rosenblatt process with varying-time delays, Random Operators and Stochastic Equations, Volume 27 (2019) no. 4, p. 213 | DOI:10.1515/rose-2019-2019
  • Lakhel, E.; Tlidi, A. Time-Dependent Neutral Stochastic Delay Partial Differential Equations Driven by Rosenblatt Process in Hilbert Space, Recent Advances in Intuitionistic Fuzzy Logic Systems, Volume 372 (2019), p. 301 | DOI:10.1007/978-3-030-02155-9_24
  • Araya, Héctor; Bahamonde, Natalia; Torres, Soledad; Viens, Frederi Donsker type theorem for fractional Poisson process, Statistics Probability Letters, Volume 150 (2019), p. 1 | DOI:10.1016/j.spl.2019.01.036
  • Saravanakumar, S.; Balasubramaniam, P. On impulsive Hilfer fractional stochastic differential system driven by Rosenblatt process, Stochastic Analysis and Applications, Volume 37 (2019) no. 6, p. 955 | DOI:10.1080/07362994.2019.1629301
  • Radchenko, V. M. Averaging principle for equation driven by a stochastic measure, Stochastics, Volume 91 (2019) no. 6, p. 905 | DOI:10.1080/17442508.2018.1559320
  • Ilmonen, Pauliina; Viitasaari, Lauri A Note on Distributions in the Second Chaos, Symmetry, Volume 11 (2019) no. 12, p. 1487 | DOI:10.3390/sym11121487
  • Coupek, Petr; Duncan, Tyrone E.; Maslowski, Bohdan; Pasik-Duncan, Bozenna, 2018 IEEE Conference on Decision and Control (CDC) (2018), p. 4973 | DOI:10.1109/cdc.2018.8619402
  • Li, Zhi; Yan, Litan; Zhou, Xianghui Global attracting sets and stability of neutral stochastic functional differential equations driven by Rosenblatt process, Frontiers of Mathematics in China, Volume 13 (2018) no. 1, p. 87 | DOI:10.1007/s11464-017-0672-x
  • Sakthivel, R.; Revathi, P.; Ren, Yong; Shen, Guangjun Retarded stochastic differential equations with infinite delay driven by Rosenblatt process, Stochastic Analysis and Applications, Volume 36 (2018) no. 2, p. 304 | DOI:10.1080/07362994.2017.1399801
  • Čoupek, P. Limiting measure and stationarity of solutions to stochastic evolution equations with Volterra noise, Stochastic Analysis and Applications, Volume 36 (2018) no. 3, p. 393 | DOI:10.1080/07362994.2017.1409124
  • Čoupek, Petr; Maslowski, Bohdan; Šnupárková, Jana SPDEs with Volterra Noise, Stochastic Partial Differential Equations and Related Fields, Volume 229 (2018), p. 147 | DOI:10.1007/978-3-319-74929-7_7
  • Diu Tran, T. T. Non-central limit theorems for quadratic functionals of Hermite-driven long memory moving average processes, Stochastics and Dynamics, Volume 18 (2018) no. 04, p. 1850028 | DOI:10.1142/s0219493718500284
  • Čoupek, Petr; Maslowski, Bohdan; Ondreját, Martin Lp-valued stochastic convolution integral driven by Volterra noise, Stochastics and Dynamics, Volume 18 (2018) no. 06, p. 1850048 | DOI:10.1142/s021949371850048x
  • Sun, Xichao; Yan, Litan Weak convergence to a class of multiple stochastic integrals, Communications in Statistics - Theory and Methods, Volume 46 (2017) no. 17, p. 8355 | DOI:10.1080/03610926.2016.1179758
  • Yan, Litan; Li, Yumiao; Wu, Di Approximation of the Rosenblatt process by semimartingales, Communications in Statistics - Theory and Methods, Volume 46 (2017) no. 9, p. 4556 | DOI:10.1080/03610926.2015.1088032
  • Shen, Guangjun; Yu, Qian An Optimal Approximation of Rosenblatt Sheet by Multiple Wiener Integrals, Mediterranean Journal of Mathematics, Volume 14 (2017) no. 2 | DOI:10.1007/s00009-017-0856-3
  • Čoupek, P.; Maslowski, B. Stochastic evolution equations with Volterra noise, Stochastic Processes and their Applications, Volume 127 (2017) no. 3, p. 877 | DOI:10.1016/j.spa.2016.07.003
  • Pakkanen, Mikko S.; Réveillac, Anthony Functional limit theorems for generalized variations of the fractional Brownian sheet, Bernoulli, Volume 22 (2016) no. 3 | DOI:10.3150/15-bej707
  • Fauth, Alexis; Tudor, Ciprian A. Multifractal Random Walk Driven by a Hermite Process, Handbook of High‐Frequency Trading and Modeling in Finance (2016), p. 221 | DOI:10.1002/9781118593486.ch8
  • Shen, Guangjun; Yin, Xiuwei; Yan, Litan Approximation of the Rosenblatt Sheet, Mediterranean Journal of Mathematics, Volume 13 (2016) no. 4, p. 2215 | DOI:10.1007/s00009-015-0576-5
  • Lakhel, El Hassan Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps, Random Operators and Stochastic Equations, Volume 24 (2016) no. 2, p. 113 | DOI:10.1515/rose-2016-0008
  • Hu, Yaozhong; Liu, Yanghui; Nualart, David Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions, The Annals of Applied Probability, Volume 26 (2016) no. 2 | DOI:10.1214/15-aap1114
  • Yan, Litan; Li, Yumiao; Wu, Di Approximating the Rosenblatt process by multiple Wiener integrals, Electronic Communications in Probability, Volume 20 (2015) no. none | DOI:10.1214/ecp.v20-3517
  • Krein, Christian Drift estimation with non-gaussian noise using Malliavin Calculus, Electronic Journal of Statistics, Volume 9 (2015) no. 2 | DOI:10.1214/15-ejs1101
  • Shen, Guangjun; Yin, Xiuwei; Zhu, Dongjin Weak convergence to Rosenblatt sheet, Frontiers of Mathematics in China, Volume 10 (2015) no. 4, p. 985 | DOI:10.1007/s11464-015-0458-y
  • Pronk, Matthijs; Veraar, Mark Forward integration, convergence and non-adapted pointwise multipliers, Infinite Dimensional Analysis, Quantum Probability and Related Topics, Volume 18 (2015) no. 01, p. 1550005 | DOI:10.1142/s0219025715500058
  • Anh, Vo; Leonenko, Nikolai; Olenko, Andriy On the rate of convergence to Rosenblatt-type distribution, Journal of Mathematical Analysis and Applications, Volume 425 (2015) no. 1, p. 111 | DOI:10.1016/j.jmaa.2014.12.016
  • Bojdecki, Tomasz; Gorostiza, Luis G.; Talarczyk, Anna From intersection local time to the Rosenblatt process, Journal of Theoretical Probability, Volume 28 (2015) no. 3, p. 1227 | DOI:10.1007/s10959-013-0535-7
  • Shen, Guangjun; Ren, Yong Neutral stochastic partial differential equations with delay driven by Rosenblatt process in a Hilbert space, Journal of the Korean Statistical Society, Volume 44 (2015) no. 1, p. 123 | DOI:10.1016/j.jkss.2014.06.002
  • Maejima, Makoto Classes of Infinitely Divisible Distributions and Examples, Lévy Matters V, Volume 2149 (2015), p. 1 | DOI:10.1007/978-3-319-23138-9_1
  • Arras, Benjamin A White Noise Approach to Stochastic Integration with Respect to the Rosenblatt Process, Potential Analysis, Volume 43 (2015) no. 4, p. 547 | DOI:10.1007/s11118-015-9484-3
  • Chen, Zhenlong; Xu, Lin; Zhu, Dongjin Generalized continuous time random walks and Hermite processes, Statistics Probability Letters, Volume 99 (2015), p. 44 | DOI:10.1016/j.spl.2014.12.027
  • Sun, Xichao; Cheng, Ronglong A Weak Convergence to Hermite Process by Martingale Differences, Advances in Mathematical Physics, Volume 2014 (2014), p. 1 | DOI:10.1155/2014/307819
  • Clarke De la Cerda, Jorge; Tudor, Ciprian A. Wiener integrals with respect to the Hermite random field and applications to the wave equation, Collectanea Mathematica, Volume 65 (2014) no. 3, p. 341 | DOI:10.1007/s13348-014-0108-9
  • Torres, Soledad; Tudor, Ciprian; Viens, Frederi Quadratic variations for the fractional-colored stochastic heat equation, Electronic Journal of Probability, Volume 19 (2014) no. none | DOI:10.1214/ejp.v19-2698
  • Bardet, Jean-Marc; Tudor, Ciprian Asymptotic behavior of the Whittle estimator for the increments of a Rosenblatt process, Journal of Multivariate Analysis, Volume 131 (2014), p. 1 | DOI:10.1016/j.jmva.2014.06.012
  • Kim, Iltae; Park, Hyun Suk; Kim, Yoon Tae Non-central limit theorem of the weighted power variations of Gaussian processes, Journal of the Korean Statistical Society, Volume 43 (2014) no. 2, p. 215 | DOI:10.1016/j.jkss.2013.09.001
  • Bai, Shuyang; Taqqu, Murad S. Generalized Hermite processes, discrete chaos and limit theorems, Stochastic Processes and their Applications, Volume 124 (2014) no. 4, p. 1710 | DOI:10.1016/j.spa.2013.12.011
  • Arras, Benjamin On a class of self-similar processes with stationary increments in higher order Wiener chaoses, Stochastic Processes and their Applications, Volume 124 (2014) no. 7, p. 2415 | DOI:10.1016/j.spa.2014.02.012
  • Veillette, Mark S.; Taqqu, Murad S. Properties and numerical evaluation of the Rosenblatt distribution, Bernoulli, Volume 19 (2013) no. 3 | DOI:10.3150/12-bej421
  • Maejima, Makoto; Tudor, Ciprian A. On the distribution of the Rosenblatt process, Statistics Probability Letters, Volume 83 (2013) no. 6, p. 1490 | DOI:10.1016/j.spl.2013.02.019
  • Gu, Yu; Bal, Guillaume Random homogenization and convergence to integrals with respect to the Rosenblatt process, Journal of Differential Equations, Volume 253 (2012) no. 4, p. 1069 | DOI:10.1016/j.jde.2012.05.007
  • Garzón, Johanna; Torres, Soledad; Tudor, Ciprian A. A strong convergence to the Rosenblatt process, Journal of Mathematical Analysis and Applications, Volume 391 (2012) no. 2, p. 630 | DOI:10.1016/j.jmaa.2012.02.040
  • Chen, Chao; Sun, Liya; Yan, Litan An approximation to the Rosenblatt process using martingale differences, Statistics Probability Letters, Volume 82 (2012) no. 4, p. 748 | DOI:10.1016/j.spl.2011.12.006
  • Iglesias, Pilar; San Martín, Jaime; Torres, Soledad; Viens, Frederi Option pricing under a Gamma-modulated diffusion process, Annals of Finance, Volume 7 (2011) no. 2, p. 199 | DOI:10.1007/s10436-011-0176-8
  • Bonaccorsi, S.; Tudor, C. A. Dissipative Stochastic Evolution Equations Driven by General Gaussian and Non-Gaussian Noise, Journal of Dynamics and Differential Equations, Volume 23 (2011) no. 4, p. 791 | DOI:10.1007/s10884-011-9217-2
  • Makarava, Natallia; Benmehdi, Sabah; Holschneider, Matthias Bayesian estimation of self-similarity exponent, Physical Review E, Volume 84 (2011) no. 2 | DOI:10.1103/physreve.84.021109
  • Davis, Richard A.; Lii, Keh-Shin; Politis, Dimitris N. The Rosenblatt Process, Selected Works of Murray Rosenblatt (2011), p. 29 | DOI:10.1007/978-1-4419-8339-8_6
  • Bertin, Karine; Torres, Soledad; Tudor, Ciprian A. Maximum-likelihood estimators and random walks in long memory models, Statistics, Volume 45 (2011) no. 4, p. 361 | DOI:10.1080/02331881003768750
  • Es-Sebaiy, K.; Tudor, C. A. Noncentral Limit Theorem for the Cubic Variation of a Class of Self-Similar Stochastic Processes, Theory of Probability Its Applications, Volume 55 (2011) no. 3, p. 411 | DOI:10.1137/s0040585x97984978
  • Nourdin, Ivan; Nualart, David; Tudor, Ciprian A. Central and non-central limit theorems for weighted power variations of fractional Brownian motion, Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, Volume 46 (2010) no. 4 | DOI:10.1214/09-aihp342
  • Shieh, Narn-Rueih; Xiao, Yimin Hausdorff and packing dimensions of the images of random fields, Bernoulli, Volume 16 (2010) no. 4 | DOI:10.3150/09-bej244
  • Pipiras, Vladas; Taqqu, Murad S. Regularization and integral representations of Hermite processes, Statistics Probability Letters, Volume 80 (2010) no. 23-24, p. 2014 | DOI:10.1016/j.spl.2010.09.008
  • Bardet, J.-M.; Tudor, C.A. A wavelet analysis of the Rosenblatt process: Chaos expansion and estimation of the self-similarity parameter, Stochastic Processes and their Applications, Volume 120 (2010) no. 12, p. 2331 | DOI:10.1016/j.spa.2010.08.003
  • Es-Sebaiy, Khalifa; Es-Sebaiy, Khalifa; Tudor, C A; Tudor, C A Noncentral limit theorem for the cubic variation of a class of self-similar stochastic processes, Теория вероятностей и ее применения, Volume 55 (2010) no. 3, p. 507 | DOI:10.4213/tvp4239
  • Chronopoulou, Alexandra; Viens, Frederi G.; Tudor, Ciprian A. Variations and Hurst index estimation for a Rosenblatt process using longer filters, Electronic Journal of Statistics, Volume 3 (2009) no. none | DOI:10.1214/09-ejs423
  • Torres, Soledad; Tudor, Ciprian A. Donsker Type Theorem for the Rosenblatt Process and a Binary Market Model, Stochastic Analysis and Applications, Volume 27 (2009) no. 3, p. 555 | DOI:10.1080/07362990902844371
  • Tudor, Ciprian A.; Viens, Frederi G. Variations and estimators for self-similarity parameters via Malliavin calculus, The Annals of Probability, Volume 37 (2009) no. 6 | DOI:10.1214/09-aop459

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