Mixed stochastic differential equations: Existence and uniqueness result

TL;DR

This paper proves the existence and uniqueness of solutions for multidimensional stochastic differential equations driven by fractional Brownian motion and standard Brownian motion, under weaker conditions than Lipschitz continuity.

Contribution

It introduces a novel existence and uniqueness result for complex stochastic differential equations with fractional and standard Brownian drivers, relaxing traditional Lipschitz conditions.

Findings

Established existence and uniqueness under weaker conditions

Extended results to multidimensional, time-dependent equations

Applicable to equations driven by fractional Brownian motion with H > 1/2

Abstract

In this paper we shall establish an existence and uniqueness result for solutions of multidimensional, time dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter $H > \frac{1}{2} and a multidimensional standard Brownian motion under a weaker condition than the Lipschitz one.