Mixed fractional stochastic differential equations with jumps

TL;DR

This paper studies a complex stochastic differential equation driven by fractional Brownian motion, Wiener process, and jumps, proving existence, uniqueness, and finiteness of moments for its solutions.

Contribution

It introduces and analyzes a new class of mixed fractional stochastic differential equations with jumps, establishing key theoretical properties.

Findings

Unique solution exists for the equation.

All moments of the solution are finite.

The model combines fractional Brownian motion and 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.