TY - UNPB
T1 - Local Limit Theorems for Energy Fluxes of Infinite Divisible Random Fields
AU - Márquez-Urbina, José Ulises
AU - Sauri Arregui, Orimar
PY - 2023
Y1 - 2023
N2 - 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 normalisation. 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.
AB - 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 normalisation. 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.
U2 - 10.48550/arXiv.2307.06288
DO - 10.48550/arXiv.2307.06288
M3 - Preprint
BT - Local Limit Theorems for Energy Fluxes of Infinite Divisible Random Fields
PB - arXiv
ER -