A Stability Result for Stochastic Differential Equations Driven by Fractional Brownian Motions. (5th December 2012)

• Record Type: Journal Article
• Authors: Saussereau, Bruno
• Other Names: Sulem Agnès Academic Editor.
• Is Part Of: International journal of stochastic analysis. Volume 2012(2012)
• Publication Date: 2012-12-05
• Subjects: Stochastic analysis -- Periodicals; Stochastic analysis; Periodicals; 519.22
• DOI: 10.1155/2012/281474
• Languages: English
• ISSNs: 2090-3332

Abstract

Abstract : We study the stability of the solutions of stochastic differential equations driven by fractional Brownian motions with Hurst parameter greater than half. We prove that when the initial conditions, the drift, and the diffusion coefficients as well as the fractional Brownian motions converge in a suitable sense, then the sequence of the solutions of the corresponding equations converge in Hölder norm to the solution of a stochastic differential equation. The limit equation is driven by the limit fractional Brownian motion and its coefficients are the limits of the sequence of the coefficients.