Original version
Stochastics: An International Journal of Probability and Stochastic Processes. 2022, 1-23, DOI: https://doi.org/10.1080/17442508.2021.2019738
Abstract
We investigate stochastic Volterra equations and their limiting laws. The stochastic Volterra equations we consider are driven by a Hilbert space valued Lévy 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.