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