Spatial asymptotic behaviors of fractional stochastic heat equations driven by additive L\'evy white noise

TL;DR

This paper investigates the spatial asymptotic behavior of fractional stochastic heat equations driven by additive Lévy white noise, revealing conditions under which they exhibit physical intermittency across dimensions.

Contribution

It provides explicit integral tests for spatial asymptotics and demonstrates the additive physical intermittency property in all dimensions for light-tailed Lévy noise.

Findings

Fractional stochastic heat equations show physical intermittency in all dimensions.

Explicit integral tests for spatial asymptotic behaviors are established.

Results depend on the tail behavior of the Lévy white noise.

Abstract

We establish explicit integral tests for spatial asymptotic behaviors of fractional stochastic heat equations driven by additive L\'evy white noise. Our results indicate that fractional stochastic heat equations enjoy the so-called additive physical intermittent property in all dimensions when the driven L\'evy white noise is sufficiently light-tailed. The proofs are based on heat kernel estimates for the fractional Laplacian and exact tail behaviors for Poissonian functionals associated with the driven L\'evy white noise.