Solutions of semilinear wave equation via stochastic cascades

TL;DR

This paper presents a probabilistic method using stochastic cascades to establish existence and uniqueness of solutions for quasilinear wave equations with analytic nonlinearities.

Contribution

It introduces a novel probabilistic representation for solutions of quasilinear wave equations, enabling new proofs of existence and uniqueness.

Findings

Probabilistic representation via stochastic cascades.

Existence and uniqueness of solutions proven.

Applicable to wave equations with analytic nonlinearities.

Abstract

We introduce a probabilistic representation for solutions of quasilinear wave equation with analytic nonlinearities. We use stochastic cascades to prove existence and uniqueness of the solution.