Local Limit Theorems for Energy Fluxes of Infinite Divisible Random Fields

2023/07/12 by Márquez-Urbina, José Ulises, Sauri, Orimar
#60D99 #60F99 (primary) 60E07 #60G57 #60G60 #60H05 (secondary) #60K40 #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2307.06288

Abstract

We study the local asymptotic behavior of divergence-like functionals of a family of d-dimensional Infinitely Divisible Random Fields. Specifically, we derive limit theorems of surface integrals over Lipschitz manifolds for this class of fields when the region of integration shrinks to a single point. We show that in most cases, convergence stably in distribution holds after a proper normalization. Furthermore, the limit random fields can be described in terms of stochastic integrals with respect to a Lévy basis. We additionally discuss how our results can be used to measure the kinetic energy of a possibly turbulent flow.

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