Stochastic Evolution Equations with Multiplicative Poisson Noise and Monotone Nonlinearity: A New Approach

TL;DR

This paper introduces a new method for proving existence and uniqueness of solutions to semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinearities, without coercivity assumptions.

Contribution

A novel proof technique for existence and uniqueness of mild solutions in stochastic evolution equations with Poisson noise and monotone drift, applicable to PDEs and delay equations.

Findings

Established existence and uniqueness of solutions

Applied theory to PDEs and delay differential equations

Provided concrete examples demonstrating the approach

Abstract

Semilinear stochastic evolution equations with multiplicative Poisson noise and monotone nonlinear drift are considered. We do not impose coercivity conditions on coefficients. A novel method of proof for establishing existence and uniqueness of the mild solution is proposed. Examples on stochastic partial differential equations and stochastic delay differential equations are provided to demonstrate the theory developed.