Stochastic Reaction-diffusion Equations Driven by Jump Processes

TL;DR

This paper proves the existence of weak solutions for a class of stochastic reaction-diffusion equations driven by jump processes, addressing challenges posed by non-Lipschitz noise and polynomial growth nonlinearities.

Contribution

It establishes the existence of solutions for complex stochastic PDEs with jump noise and non-Lipschitz coefficients, expanding the theoretical understanding of such equations.

Findings

Existence of weak martingale solutions proven

Handles non-Lipschitz multiplicative noise

Addresses polynomial growth nonlinearities

Abstract

We establish the existence of weak martingale solutions to a class of second order parabolic stochastic partial differential equations. The equations are driven by multiplicative jump type noise, with a non-Lipschitz multiplicative functional. The drift in the equations contains a dissipative nonlinearity of polynomial growth.