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

2019/03/12 by Fred Espen Benth, Benth, Fred Espen, Nils Detering +3
Economics, Econometrics and Finance · #60H15 #60H20 #60Hxx #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1903.05045

openalex publication_date 2019/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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