Fractional stochastic differential equation with discontinuous diffusion

TL;DR

This paper investigates a fractional stochastic differential equation with discontinuous diffusion coefficients driven by fractional Brownian motion, providing an approximation method and aiming to define a fractional skew Brownian motion.

Contribution

It introduces a fractional SDE with discontinuous coefficients and proposes an approximation, advancing the understanding of fractional skew Brownian motion.

Findings

Established an approximation scheme for the fractional SDE

Paved the way for defining fractional skew Brownian motion

Extended stochastic calculus to discontinuous coefficients

Abstract

In this paper we study a stochastic differential equation driven by a fractional Brownian motion with a discontinuous coefficient. We also give an approximation to the solution of the equation. This is a first step to define a fractional version of the skew Brownian motion.