Large deviations and Berry–Esseen inequalities for estimators in nonhomogeneous diffusion driven by fractional Brownian motion

References

[1] J. P. N. Bishwal, Large deviations and Berry–Esseen inequalities for estimators in nonlinear nonhomogeneous diffusions, REVSTAT 5 (2007), no. 3, 249–267. Suche in Google Scholar

[2] J. P. N. Bishwal, Parameter Estimation in Stochastic Differential Equations, Lecture Notes in Math. 1923, Springer, Berlin, 2008. 10.1007/978-3-540-74448-1Suche in Google Scholar

[3] V. Borkar and A. Bagchi, Parameter estimation in continuous-time stochastic processes, Stochastics 8 (1982/83), no. 3, 193–212. 10.1080/17442508208833238Suche in Google Scholar

[4] L. Coutin and L. Decreusefond, Stochastic differential equations driven by a fractional Brownian motion, Technical Report 97C004, ENST Paris, 1997. Suche in Google Scholar

[5] L. Decreusefond and A. S. Üstünel, Fractional Brownian motion: Theory and applications, ESAIM Proc. 5 (1998), 75–86. 10.1051/proc:1998014Suche in Google Scholar

[6] L. Decreusefond and A. S. Üstünel, Stochastic analysis of the fractional Brownian motion, Potential Anal. 10 (1999), no. 2, 177–214. 10.1023/A:1008634027843Suche in Google Scholar

[7] P. Hall and C. C. Heyde, Martingale Limit Theory and its Application, Academic Press, New York, 1980. Suche in Google Scholar

[8] H. Hult, Approximating some Volterra type stochastic integrals with applications to parameter estimation, Stochastic Process. Appl. 105 (2003), no. 1, 1–32. 10.1016/S0304-4149(02)00250-8Suche in Google Scholar

[9] I. A. Ibragimov and R. Z. Has’minskiĭ, Statistical Estimation: Asymptotic Theory, Springer, New York, 1981. 10.1007/978-1-4899-0027-2Suche in Google Scholar

[10] T. Kailath, A. Segall and M. Zakai, Fubini-type theorems for stochastic integrals, Sankhyā Ser. A 40 (1978), no. 2, 138–143. Suche in Google Scholar

[11] Y. A. Kutoyants, Estimation of a parameter of a diffusion type process, Theor. Probab. Appl. 23 (1978), 611–619. 10.1137/1123076Suche in Google Scholar

[12] Y. A. Kutoyants, Parameter Estimation for Stochastic Processes, Heldermann, Berlin, 1984. Suche in Google Scholar

[13] D. Levanony, A. Shwartz and O. Zeitouni, Recursive identification in continuous-time stochastic processes, Stochastic Process. Appl. 49 (1994), no. 2, 245–275. 10.1016/0304-4149(94)90137-6Suche in Google Scholar

[14] P. Malliavin, Stochastic calculus of variation and hypoelliptic operators, Proceedings of the International Symposium on Stochastic Differential Equations (Kyoto 1976), Wiley, New York (1978), 195–263. Suche in Google Scholar

[15] R. Michel and J. Pfanzagl, The accuracy of the normal approximation for minimum contrast estimates, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 18 (1971), 73–84. 10.1007/BF00538488Suche in Google Scholar

[16] M. N. Mishra, The Bernstein–von Mises theorem for a class of nonhomogeneous diffusion processes, Statist. Decisions 7 (1989), no. 1–2, 153–165. 10.1524/strm.1989.7.12.153Suche in Google Scholar

[17] M. N. Mishra and B. L. S. Prakasa Rao, Asymptotic study of the maximum likelihood estimator for nonhomogeneous diffusion processes, Statist. Decisions 3 (1985), no. 3–4, 193–203. 10.1524/strm.1985.3.34.193Suche in Google Scholar

[18] A. Novikov and E. Valkeila, On some maximal inequalities for fractional Brownian motions, Statist. Probab. Lett. 44 (1999), no. 1, 47–54. 10.1016/S0167-7152(98)00290-9Suche in Google Scholar

[19] D. Nualart, The Malliavin Calculus and Related Topics, Probab. Appl. (N. Y.), Springer, New York, 1995. 10.1007/978-1-4757-2437-0Suche in Google Scholar

[20] D. Nualart and Y. Ouknine, Regularization of differential equation by fractional noise, Stoch. Proc. Appl. 102 (2002), 103–116. 10.1016/S0304-4149(02)00155-2Suche in Google Scholar

[21] B. L. S. Prakasa Rao, Statistical Inference for Fractional Diffusion Processes, John Wiley & Sons, Chichester, 2010. Suche in Google Scholar

[22] S. G. Samko, A. A. Kilbas and O. I. Marichev, Fractional Integrals and Derivatives, Gordon and Breach Science, Yverdon, 1993. Suche in Google Scholar

[23] C. A. Tudor and F. G. Viens, Statistical aspects of the fractional stochastic calculus, Ann. Statist. 35 (2007), no. 3, 1183–1212. 10.1214/009053606000001541Suche in Google Scholar