On mixed fractional SDEs with discontinuous drift coefficient

Abstract

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient.

References in corpus (1)

• Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients

Cited by in corpus (1)

• Regularization of differential equations by two fractional noises