Approximation of solutions of stochastic differential equations with fractional Brownian motion by solutions of random ordinary differential equations
- 133 Downloads
We prove a general theorem on the convergence of solutions of stochastic differential equations. As a corollary, we obtain a result concerning the convergence of solutions of stochastic differential equations with absolutely continuous processes to a solution of an equation with Brownian motion.
Unable to display preview. Download preview PDF.
- 4.A. A. Ruzmaikina, “Stieltjes integrals of Hölder continuous functions with applications to fractional Brownian motion,” J. Statist. Phys., No. 5–6, 1049–1069 (2000).Google Scholar
- 6.I. Nourdin, “A simple theory for the study of SDEs driven by a fractional Brownian motion, in dimension one,” in: Sémin. Probab. XLI, Some Papers and Selected Contributions of the Seminars in Nancy 2005 and Luminy 2006 (Lecture Notes in Mathematics, 1934), Springer, Berlin (2008), pp. 181–197.Google Scholar
- 12.Yu. S. Mishura, “Quasilinear stochastic differential equations with fractional Brownian component,” Teor. Imovir. Mat. Stat., No. 68, 95–106 (2004).Google Scholar
- 18.T. Androshchuk, “Approximation of a stochastic integral over fractional Brownian motion by integrals over absolutely continuous processes,” Teor. Imovir. Mat. Stat., No. 73, 11–20 (2005).Google Scholar
- 19.S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Their Applications [in Russian], Nauka i Tekhnika, Minsk (1987).Google Scholar