Benth, Fred Espen, Detering, Nils, Eisenberg, Paul. 2022. Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations. Stochastics. 94

RIS

@ARTICLE{Benth2022,
title = {Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations},
author = {Fred Espen Benth and Nils Detering and Paul Eisenberg},
year = {2022},
doi = {https://doi.org/10.1080/17442508.2021.2019738},
url = {https://www.tandfonline.com/doi/full/10.1080/17442508.2021.2019738},
volume = {94},
language = {EN},
journal = {Stochastics},
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.},
}