Approximation of a stochastic wave equation in dimension three, with application to a support theorem in H\"{o}lder norm

TL;DR

This paper characterizes the support of the solution's law in Hölder norm for a 3D stochastic wave equation, using an approximation theorem based on regularized noise sequences.

Contribution

It provides a new support theorem in Hölder norm for solutions to 3D stochastic wave equations through probabilistic convergence of regularized approximations.

Findings

Support in Hölder norm characterized for 3D stochastic wave solutions

Approximation theorem established for regularized noise sequences

Convergence in probability demonstrated for evolution equations

Abstract

A characterization of the support in H\"{o}lder norm of the law of the solution to a stochastic wave equation with three-dimensional space variable is proved. The result is a consequence of an approximation theorem, in the convergence of probability, for a sequence of evolution equations driven by a family of regularizations of the driving noise.