# Stochastic Volterra integral equations and a class of first order stochastic partial differential equations

## TL;DR

This paper studies stochastic Volterra equations driven by Levy noise, exploring their limiting behavior and linking solutions to stochastic PDEs through an embedding approach.

## Contribution

It introduces a novel embedding method to analyze stochastic Volterra equations with non-linear kernels and Levy noise, connecting them to stochastic PDEs.

## Key findings

- Established abstract results for stochastic Volterra equations.
- Derived conditions for solutions in specific function spaces.
- Linked solutions of Volterra equations to boundary values of stochastic PDEs.

## Abstract

We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued \Levy noise and integration kernels may have non-linear dependence on the current state of the process. Our method is based on an embedding into a Hilbert space of functions which allows to represent the solution of the Volterra equation as the boundary value of a solution to a stochastic partial differential equation. We first gather abstract results and give more detailed conditions in more specific function spaces.