no. 5
LAN property for ergodic diffusions with discrete observations
Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 5, pp. 711-737. 
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     author = {Gobet, Emmanuel},
     title = {LAN property for ergodic diffusions with discrete observations},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {711--737},
     publisher = {Elsevier},
     volume = {38},
     number = {5},
     year = {2002},
     mrnumber = {1931584},
     zbl = {1018.60076},
     language = {en},
     url = {http://www.numdam.org/item/AIHPB_2002__38_5_711_0/}
}
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Gobet, Emmanuel. LAN property for ergodic diffusions with discrete observations. Annales de l'I.H.P. Probabilités et statistiques, Tome 38 (2002) no. 5, pp. 711-737. http://www.numdam.org/item/AIHPB_2002__38_5_711_0/

[1] D.G. Aronson, Bounds for the fundamental solution of a parabolic equation, Bull. Amer. Math. Soc. 73 (1967) 890-903. | MR | Zbl

[2] D. Dacunha-Castelle, D. Florens-Zmirou, Estimation of the coefficient of a diffusion from discrete observations, Stochastics 19 (1986) 263-284. | MR | Zbl

[3] G. Donhal, On estimating the diffusion coefficient, J. Appl. Probab. 24 (1987) 105-114. | MR | Zbl

[4] D. Florens-Zmirou, Approximate discrete time schemes for statistics of diffusion processes, Statistics 20 (1989) 547-557. | MR | Zbl

[5] A. Friedman, Stochastic Differential Equations and Applications, Vol. 1, Academic Press, New York, 1975. | MR | Zbl

[6] V. Genon-Catalot, Maximum contrast estimation for diffusion processes from discrete observations, Statistics 21 (1990) 99-116. | MR | Zbl

[7] V. Genon-Catalot, J. Jacod, On the estimation of the diffusion coefficient for multidimensional diffusion processes, Ann. Inst. H. Poincaré (Probab. Statist.) 29 (1993) 119-151. | Numdam | MR | Zbl

[8] V. Genon-Catalot, J. Jacod, Estimation of the diffusion coefficient for diffusion processes: random sampling, Scandinavian J. Statist. 21 (1994) 193-221. | MR | Zbl

[9] E. Gobet, Local asymptotic mixed normality property for elliptic diffusion, Bernouilli 7 (6) (2001) 899-912. | MR | Zbl

[10] J. Hajek, Local asymptotic minimax admissibility in estimation, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles, University of California Press, 1971, pp. 175-194. | MR | Zbl

[11] R.Z. Has'Minskii, Stochastic Stability of Differential Equations, Sijthoff & Noordhoff, 1980. | MR

[12] R. Höpfner, J. Jacod, L. Ladelli, Local asymptotic normality and mixed normality for Markov statistical models, Probab. Theory Related Fields 86 (1990) 105-129. | MR | Zbl

[13] J. Jacod, Private communication.

[14] J. Jacod, A.N. Shiryaev, Limit Theorems for Stochastic Processes, Springer, Berlin, 1987. | MR | Zbl

[15] I. Karatzas, S.E. Shreve, Brownian Motion and Stochastic Calculus, Springer, 1998. | MR | Zbl

[16] M. Kessler, Estimation of an ergodic diffusion from discrete observations, Scandinavian J. Statist. 24 (1997) 211-229. | MR | Zbl

[17] H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, in: Ecole d'Eté de Probabilités de St-Flour XII, 1982, Lecture Notes in Math., 1097, Springer, 1984, pp. 144-305. | MR | Zbl

[18] L. Le Cam, Limits of experiments, in: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Berkeley and Los Angeles, University of California Press, 1971, pp. 245-261. | Zbl

[19] L. Le Cam, G.L. Yang, Asymptotics in Statistics, Springer, 1990. | MR | Zbl

[20] T.J. Lyons, W.A. Zheng, On conditional diffusion processes, Proc. Royal Soc. Edinburgh 115 A (1990) 243-255. | MR | Zbl

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

[22] B.L.S. Prakasa Rao, Asymptotic theory for non-linear least square estimator for diffusion processes, Math. Operationsforsch. Statist. Ser. Stat. 14 (1983) 195-209. | MR | Zbl

[23] B.L.S. Prakasa Rao, Statistical Inference for Diffusion Type Processes, Kendall's Library of Statistics, 8, Edward Arnold, London, Oxford University Press, New York, 1999. | MR | Zbl

[24] N. Yoshida, Estimation for diffusion processes from discrete observations, J. Multivariate Anal. 41 (1992) 220-242. | MR | Zbl

[25] N. Yoshida, Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe, Probab. Theory Related Fields 92 (1992) 275-311. | Zbl

[26] N. Yoshida, Asymptotic expansions for perturbed systems on Wiener space, maximum likelihood estimators, J. Multivariate Anal. 57 (1996) 1-36. | MR | Zbl