Multivalued stochastic partial differential-integral equations via backward doubly stochastic differential equations driven by a L\'evy process

TL;DR

This paper establishes existence and uniqueness results for a class of backward doubly stochastic differential equations driven by Lévy processes, and applies these to prove the existence of solutions for multivalued stochastic partial differential-integral equations.

Contribution

It introduces a novel approach using Yosida approximation for BDSDEs with subdifferential operators driven by Lévy processes, extending the theory to multivalued MSPIDEs.

Findings

Proved existence and uniqueness of solutions for the considered BDSDEs.

Established the existence of stochastic viscosity solutions for MSPIDEs.

Extended stochastic PDE theory to include Lévy-driven multivalued equations.

Abstract

In this paper, we deal with a class of backward doubly stochastic differential equations (BDSDEs, in short) involving subdifferential operator of a convex function and driven by Teugels martingales associated with a L\'evy process. We show the existence and uniqueness result by means of Yosida approximation. As an application, we give the existence of stochastic viscosity solution for a class of multivalued stochastic partial differential-integral equations (MSPIDEs, in short).