no. 6
Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter H∈(0,1 2)
Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1049-1081. 
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     title = {Stochastic integral of divergence type with respect to fractional brownian motion with {Hurst} parameter $H\in (0,\frac{1}{2})$},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1049--1081},
     publisher = {Elsevier},
     volume = {41},
     number = {6},
     year = {2005},
     doi = {10.1016/j.anihpb.2004.09.004},
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     zbl = {1083.60027},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.anihpb.2004.09.004/}
}
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Cheridito, Patrick; Nualart, David. Stochastic integral of divergence type with respect to fractional brownian motion with Hurst parameter $H\in (0,\frac{1}{2})$. Annales de l'I.H.P. Probabilités et statistiques, Tome 41 (2005) no. 6, pp. 1049-1081. doi : 10.1016/j.anihpb.2004.09.004. http://www.numdam.org/articles/10.1016/j.anihpb.2004.09.004/

[1] E. Alòs, J.A. León, D. Nualart, Stochastic Stratonovich calculus for fractional Brownian motion with Hurst parameter less than 1/2, Taiwanese J. Math. 5 (3) (2001) 609-632. | MR | Zbl

[2] E. Alòs, O. Mazet, D. Nualart, Stochastic calculus with respect to fractional Brownian motion with Hurst parameter lesser than 1/2, Stochastic Process Appl. 86 (1) (2000) 121-139. | MR | Zbl

[3] E. Alòs, O. Mazet, D. Nualart, Stochastic calculus with respect to Gaussian processes, Ann. Probab. 29 (2) (2001) 766-801. | MR | Zbl

[4] C. Bender, An Itô formula for generalized functionals of a fractional Brownian motion with arbitrary Hurst parameter, Stochastic Process Appl. 104 (1) (2003) 81-106. | MR | Zbl

[5] S. Berman, Local nondeterminism and local times of Gaussian processes, Indiana Univ. Math. J. 23 (1973) 69-94. | MR | Zbl

[6] P. Carmona, L. Coutin, G. Montseny, Stochastic integration with respect to fractional Brownian motion, Ann. Inst. H. Poincaré Probab. Statist. 39 (1) (2003) 27-68. | Numdam | MR | Zbl

[7] L. Coutin, D. Nualart, C.A. Tudor, Tanaka formula for the fractional Brownian motion, Stochastic Process Appl. 94 (2) (2001) 301-315. | MR | Zbl

[8] L. Coutin, Z. Qian, Stochastic analysis, rough path analysis and fractional Brownian motions, Probab. Theory Related Fields 122 (1) (2002) 108-140. | MR | Zbl

[9] L. Decreusefond, A.S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (2) (1999) 177-214. | MR | Zbl

[10] T.E. Duncan, Y. Hu, B. Pasik-Duncan, Stochastic calculus for fractional Brownian motion I. Theory, SIAM J. Control Optim. 38 (2) (2000) 582-612. | MR | Zbl

[11] B. Gaveau, P. Trauber, L'integrale stochastique comme opérateur de divergence dans l'espace fonctionnel, J. Funct. Anal. 46 (2) (1982) 230-238. | MR | Zbl

[12] M. Gradinaru, F. Russo, P. Vallois, Generalized covariations, local time and Stratonovich Itô’s formula for fractional Brownian motion with Hurst index H≥1/4, Ann. Probab. 31 (4) (2003) 1772-1820. | Zbl

[13] M. Gradinaru, I. Nourdin, F. Russo, P. Vallois, m-order integrals and generalized Itô's formula: the case of a fractional Brownian motion with any Hurst index, Preprint, 2002.

[14] Y. Hu, Probability structure preserving and absolute continuity, Ann. Inst. H. Poincaré 38 (4) (2002) 557-580. | Numdam | MR | Zbl

[15] Y. Hu, B. Øksendal, Fractional white noise calculus and applications to finance, Inf. Dim. Anal. Quant. Probab. Rel. Top. 6 (1) (2003) 1-32. | MR | Zbl

[16] K. Itô, Stochastic integral, Proc. Imperial Acad. Tokyo 20 (1944) 519-524. | MR | Zbl

[17] S.J. Lin, Stochastic analysis of fractional Brownian motions, Stochastics Stochastics Rep. 55 (1995) 121-140. | MR | Zbl

[18] Sh.R. Liptser, A.N. Shiryaev, Theory of Martingales, Kluwer Academic, Dordrecht, 1989. | MR | Zbl

[19] S. Maheswaran, C.A. Sims, Empirical implications of arbitrage-free asset markets, in: Phillips P.C.B. (Ed.), Models, Methods and Applications of Econometrics, Blackwell, 1993.

[20] P. Malliavin, Stochastic Analysis, Springer, 1997. | MR | Zbl

[21] T. Mikosch, R. Norvaiša, Stochastic integral equations without probability, Bernoulli 6 (3) (2000) 401-434. | MR | Zbl

[22] D. Nualart, The Malliavin Calculus and Related Topics, Springer, 1995. | MR | Zbl

[23] D. Nualart, E. Pardoux, Stochastic calculus with anticipating integrands, Probab. Theory Related Fields 78 (4) (1988) 535-581. | MR | Zbl

[24] V. Pipiras, M.S. Taqqu, Integration questions related to fractional Brownian motion, Probab. Theory Related Fields 118 (2) (2000) 251-291. | MR | Zbl

[25] V. Pipiras, M.S. Taqqu, Are classes of deterministic integrands for fractional Brownian motion on an interval complete?, Bernoulli 7 (6) (2001) 873-897. | MR | Zbl

[26] N. Privault, Skorohod stochastic integration with respect to non-adapted processes on Wiener space, Stochastics Stochastics Rep. 65 (1998) 13-39. | MR | Zbl

[27] D. Revuz, M. Yor, Continuous Martingales and Brownian Motion, Springer, 1999. | MR | Zbl

[28] F. Russo, P. Vallois, Forward, backward and symmetric stochastic integration, Probab. Theory Related Fields 97 (3) (1993) 403-421. | MR | Zbl

[29] F. Russo, P. Vallois, The generalized covariation process and Itô formula, Stochastic Process Appl. 59 (1) (1995) 81-104. | MR | Zbl

[30] F. Russo, P. Vallois, Itô formula for C 1 -functions of semimartingales, Probab. Theory Related Fields 104 (1) (1996) 27-41. | MR | Zbl

[31] L.C.G. Rogers, Arbitrage with fractional Brownian motion, Math. Finance 7 (1) (1997) 95-105. | MR | Zbl

[32] F.G. Samko, A.A. Kilbas, O.I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach, 1993. | MR | Zbl

[33] L.C. Young, An inequality of the Hölder type, connected with Stieltjes integration, Acta Math. (Sweden) 67 (1936) 251-282. | MR | Zbl

[34] M. Zähle, Integration with respect to fractal functions and stochasic calculus. I, Probab. Theory Related Fields 111 (3) (1998) 333-374. | MR | Zbl

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