# Local Nondeterminism and the Exact Modulus of Continuity for Stochastic Wave Equation

## TL;DR

This paper establishes the strong local nondeterminism property for solutions of the stochastic wave equation driven by Gaussian noise and uses it to derive the exact uniform modulus of continuity.

## Contribution

It introduces the concept of strong local nondeterminism for the stochastic wave equation and determines the exact modulus of continuity of its solutions.

## Key findings

- Solution satisfies strong local nondeterminism
- Derived the exact uniform modulus of continuity
- Provides insights into the regularity of stochastic wave solutions

## Abstract

We consider the linear stochastic wave equation driven by a Gaussian noise. We show that the solution satisfies a certain form of strong local nondeterminism and we use this property to derive the exact uniform modulus of continuity for the solution.