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

Fred Espen Benth, Nils Detering*, Paul Krühner

*Korrespondierende*r Autor*in für diese Arbeit

Publikation: Wissenschaftliche FachzeitschriftOriginalbeitrag in FachzeitschriftForschungBegutachtung

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.
OriginalspracheEnglisch
Seiten (von - bis)1054-1076
FachzeitschriftStochastics
Jahrgang94
Ausgabenummer7
DOIs
PublikationsstatusVeröffentlicht - 2022

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