Delocalization of a $(1+1)$-dimensional stochastic wave equation

TL;DR

This paper demonstrates that unlike many parabolic stochastic PDEs, a broad class of one-dimensional stochastic wave equations do not exhibit local linearization, highlighting fundamental differences in their behavior.

Contribution

The paper establishes that a large family of one-dimensional stochastic wave equations lack the local linearization property common in parabolic stochastic PDEs.

Findings

Stochastic wave equations in 1D do not locally linearize.

Contrast with parabolic stochastic PDEs.

Highlights fundamental differences in behavior.

Abstract

A noteworthy property of many parabolic stochastic PDEs is that they locally linearize (Foondun, Khoshnevisan and Mahboubi (2015), Hairer (2013, 2014), Hairer and Pardoux (2015), Khoshnevisan, Swanson, Xiao and Zhang (2013)). We prove that, by contrast, a large family of stochastic wave equations in dimension one do not possess this important property.