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

Benth, Fred Espen, Detering, Nils and Kruehner, Paul (2022) Stochastic Volterra integral equations and a class of first-order stochastic partial differential equations. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 94 (7). pp. 1054-1076.

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Official URL: http://dx.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 \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.

Item Type:	Article
Additional Information:	17 pages
Uncontrolled Keywords:	Stochastic partial differential equation, limiting law, Hilbert space, Levy noise, stochastic Volterra integral equation
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	30 May 2022 14:39
Last Modified:	18 Jan 2023 21:00
DOI:	10.1080/17442508.2021.2019738
Open Access URL:	https://arxiv.org/pdf/1903.05045.pdf
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3155700