Hitting times for the stochastic wave equation with fractional-colored noise

TL;DR

This paper investigates the regularity and hitting probabilities of solutions to the stochastic wave equation driven by fractional-colored noise, providing precise bounds using geometric measures.

Contribution

It offers new sharp regularity results and bounds for hitting probabilities of the stochastic wave equation with fractional-colored noise, linking probabilistic behavior to geometric measures.

Findings

Established sharp regularity results for the solution.

Derived upper and lower bounds for hitting probabilities.

Connected hitting probabilities to Hausdorff measure and Newtonian capacity.

Abstract

We give sharp regularity results for the solution to the stochastic wave equation with linear fractional-colored noise. We apply these results in order to establish upper and lower bound for the hitting probabilities of the solution in terms of the Hausdorff measure and of the Newtonian capacity.