Mixed fractional stochastic differential equations with jumps

Abstract

In this paper, we consider a stochastic differential equation driven by a fractional Brownian motion (fBm) and a Wiener process and having jumps. We prove that this equation has a unique solution and show that all its moments are finite.

References in corpus (3)

• Stochastic Differential Equations Driven by Fractional Brownian Motion and Standard Brownian Motion
• Mixed stochastic differential equations with long-range dependence: existence, uniqueness and convergence of solutions
• Stochastic differential equation involving Wiener process and fractional Brownian motion with Hurst index $H>1/2$

Cited by in corpus (4)

• Malliavin regularity of solutions to mixed stochastic differential equations
• Averaging Principles for Mixed Fast-Slow Systems Driven by Fractional Brownian Motion
• Existence and uniqueness of mild solution to fractional stochastic heat equation
• Pathwise unique solutions and stochastic averaging for mixed stochastic partial differential equations driven by fractional Brownian motion and Brownian motion