Approximation of solutions of SDEs driven by a fractional Brownian motion, under pathwise uniqueness
Volume 3, Issue 4 (2016), pp. 303–313
Pub. online: 20 December 2016
Type: Research Article
Open Access
Open Access
1
This author is supported by the CNRST “Centre National pour la Recherche Scientifique et Technique”, grant No. I 003/034, Rabat, Morocco.
Received
29 July 2016
29 July 2016
Revised
12 December 2016
12 December 2016
Accepted
13 December 2016
13 December 2016
Published
20 December 2016
20 December 2016
Abstract
Our aim in this paper is to establish some strong stability properties of a solution of a stochastic differential equation driven by a fractional Brownian motion for which the pathwise uniqueness holds. The results are obtained using Skorokhod’s selection theorem.
References
Bahlali, K., Mezerdi, B., Ouknine, Y.: Pathwise uniqueness and approximation of solutions of stochastic differential equations. In: Azéma, J., Yor, M., Émery, M., Ledoux, M. (eds.) Séminaire de Probabilités XXXII. Springer, Berlin (1998). MR1655150. doi:10.1007/BFb0101757
Banos, D., Nilssen, T., Proske, F.: Strong existence and higher order Fréchet differentiability of stochastic flows of fractional Brownian motion driven SDE with singular drift. arXiv:1509.01154 (2015)
Decreusefond, L., Üstünel, A.S.: Stochastic analysis of the fractional Brownian motion. Potential Anal. 10, 177–214 (1998). MR1677455. doi:10.1023/A:1008634027843
Ikeda, N., Watanabe, S.: Stochastic Differential Equations and Diffusion Processes. North-Holland, Amsterdam (1981). MR1011252
Kolmogorov, A.N.: Wienersche Spiralen und einige andere interessante Kurven im Hilbertschen Raum. C. R. (Dokl.) Acad. Sci. URSS 26, 115–118 (1940). MR0003441
Mandelbrot, B.-B., Van Ness, J.-W.: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10, 422–437 (1968). MR0242239
Nualart, D.: The Malliavin Calculus and Related Topics. Springer, New York (2006). MR2200233
Nualart, D., Ouknine, Y.: Regularizing differential equations by fractional noise. Stoch. Process. Appl. 102, 103–116 (2002). MR1934157. doi:10.1016/S0304-4149(02)00155-2
