Stochastic PDEs in S' for SDEs driven by Lévy noise

Article Type

Research Article

Publication Title

Random Operators and Stochastic Equations

Abstract

In this article we show that a finite-dimensional stochastic differential equation driven by a Lévy noise can be formulated as a stochastic partial differential equation (SPDE) driven by the same Lévy noise. We prove the existence result for such an SPDE by Itô’s formula for translation operators, and the uniqueness by an adapted form of “Monotonicity inequality”, proved earlier in the diffusion case. As a consequence, the solutions that we construct have the “translation invariance” property.

First Page

217

Last Page

226

DOI

10.1515/rose-2020-2041

Publication Date

9-1-2020

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