Spatial asymptotic behaviors of fractional stochastic heat equations driven by additive Lévy white noise

2024/05/18 by Yuichi Shiozawa, Jian Wang, Shiozawa, Yuichi +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2405.11291

openalex publication_date 2024/05/18 · openalex created_date 2024/05/22 · openalex updated_date 2026/07/28

Abstract

We establish explicit integral tests for spatial asymptotic behaviors of fractional stochastic heat equations driven by additive Lévy white noise. Our results indicate that fractional stochastic heat equations enjoy the so-called additive physical intermittent property in all dimensions when the driven Lévy 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 Lévy white noise.

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