On the local linearization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing

TL;DR

This paper proves a bi-parameter linear localization property for the one-dimensional stochastic wave equation driven by multiplicative space-time white noise, advancing understanding of its local behavior.

Contribution

It introduces a novel bi-parameter linear localization result for the stochastic wave equation with multiplicative noise, a new insight in stochastic PDE analysis.

Findings

Establishes bi-parameter linear localization for the equation

Provides new tools for analyzing stochastic wave equations with multiplicative noise

Enhances understanding of local behavior in stochastic PDEs

Abstract

In this note, we establish a bi-parameter linear localization of the one-dimensional stochastic wave equation with a multiplicative space-time white noise forcing.