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

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arxiv 2405.11291 v1 pith:QRPEL2N2 submitted 2024-05-18 math.PR

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

classification math.PR
keywords drivenfractionalheatnoisewhiteadditivebehaviorsequations
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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.

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