Existence of weak solutions for a class of semilinear stochastic wave equations

TL;DR

This paper establishes the existence of weak solutions for a broad class of stochastic semilinear wave equations on bounded domains, driven by possibly discontinuous martingales, advancing understanding in stochastic PDEs.

Contribution

It proves the existence of weak solutions for stochastic semilinear wave equations driven by discontinuous martingales, a generalization in stochastic PDE theory.

Findings

Existence of weak solutions proven for a broad class of equations.

Applicable to equations driven by discontinuous martingales.

Advances the mathematical understanding of stochastic wave equations.

Abstract

We prove existence of weak solutions (in the probabilistic sense) for a general class of stochastic semilinear wave equations on bounded domains of $R^d$ driven by a possibly discontinuous square integrable martingale.