Approximation of solutions of SDEs driven by a fractional Brownian motion, under pathwise uniqueness

TL;DR

This paper investigates the stability of solutions to stochastic differential equations driven by fractional Brownian motion, assuming pathwise uniqueness, and employs Skorokhod's theorem to establish these properties.

Contribution

It provides new stability results for SDEs driven by fractional Brownian motion under the assumption of pathwise uniqueness, using Skorokhod's selection theorem.

Findings

Established strong stability properties of solutions

Demonstrated the use of Skorokhod's theorem in this context

Provided theoretical insights into fractional Brownian motion-driven SDEs

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.