Mixed stochastic delay differential equations

TL;DR

This paper studies stochastic delay differential equations driven by Holder continuous and Wiener processes, proving unique solvability, moment finiteness, and establishing a limit theorem under general conditions.

Contribution

It introduces new conditions ensuring existence, uniqueness, and moment bounds for solutions to stochastic delay differential equations driven by complex noise.

Findings

Unique solvability under general assumptions

Conditions for finiteness of moments

A new limit theorem for solutions

Abstract

We consider a stochastic delay differential equation driven by a Holder continuous process and a Wiener process. Under fairly general assumptions on its coefficients, we prove that this equation is uniquely solvable. We also give sufficient conditions for finiteness of its moments and establish a limit theorem.