Stochastic differential equations driven by additive Volterra-L\'evy and Volterra-Gaussian noises

TL;DR

This paper investigates the existence and uniqueness of solutions to stochastic differential equations driven by Volterra processes with Le9vy noise, focusing on smoothness properties and generalizations of fractional Brownian motion.

Contribution

It provides new results on the well-posedness of SDEs driven by Volterra-Le9vy and Volterra-Gaussian processes, including detailed analysis of process smoothness.

Findings

Established conditions for existence and uniqueness of solutions

Analyzed smoothness properties of Volterra-driven processes

Extended fractional Brownian motion representations

Abstract

We study the existence and uniqueness of solutions to stochastic differential equations with Volterra processes driven by L\'evy noise. For this purpose, we study in detail smoothness properties of these processes. Special attention is given to two kinds of Volterra-Gaussian processes that generalize the compact interval representation of fractional Brownian motion and to stochastic equations with such processes.