An $L^p$-theory of non-divergence form SPDEs driven by L\'evy processes

TL;DR

This paper develops an $L^p$-theory for non-divergence form SPDEs driven by Lévy processes, establishing existence and uniqueness of solutions in Sobolev spaces with random coefficients.

Contribution

It introduces a novel $L^p$-theory for SPDEs driven by Lévy processes, handling random coefficients depending on time and space.

Findings

Proves existence and uniqueness of solutions in Sobolev spaces.

Handles SPDEs with random coefficients in non-divergence form.

Extends classical theories to Lévy-driven stochastic PDEs.

Abstract

In this paper we present an $L^p$-theory for the stochastic partial differential equations (SPDEs in abbreciation) driven by L\'e{}vy processes. Existence and uniqueness of solutions in Sobolev spaces are obtained. The coefficients of SPDEs under consideration are random functions depending on time and space variables.