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

Fred Espen Benth; Nils Detering; Paul Kruehner

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arXiv · 1903.05045

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

Fred Espen Benth·Nils Detering·Paul Kruehner

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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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BibTeX RIS

Fred Espen Benth, Nils Detering, Paul Kruehner. 2019-03-12. Stochastic Volterra integral equations and a class of first order stochastic partial differential equations. https://arxiv.org/abs/1903.05045

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