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.

Theorems & Definitions (16)

• Lemma 2.1
• Proposition 2.2
• proof
• Theorem 2.4
• proof
• Theorem 3.1
• proof
• Theorem 4.1
• Remark 4.2
• Lemma 4.3