An $L^2$-theory on SPDE driven by L\'evy processes

TL;DR

This paper develops an $L^2$-theory for stochastic partial differential equations driven by Lévy processes, accommodating random coefficients with no smoothness assumptions, advancing the mathematical understanding of such SPDEs.

Contribution

It introduces an $L^2$-theory for SPDEs driven by Lévy processes with non-smooth, random coefficients, expanding the analytical framework for these equations.

Findings

Established existence and uniqueness results for solutions.

Extended the theory to equations with non-smooth, random coefficients.

Provided a foundation for further analytical and numerical studies.

Abstract

In this paper we develop an $L_2$-theory for stochastic partial differential equations driven by L\'evy processes. The coefficients of the equations are random functions depending on time and space variables, and no smoothness assumption of the coefficients is assumed.