Asymptotic expansion of the nonlocal heat content

2022/02/23 by Tomasz Grzywny, Grzywny, Tomasz, Julia Lenczewska +1
Economics, Econometrics and Finance · Mathematics · #35K05 #60G51 #60G52 #60J76 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Probability (math.PR) #Stochastic processes and financial applications #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2202.11662

openalex publication_date 2022/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X=\X_t\_{t≥ 0} be a Lévy process in ℝ^d and Ω be an open subset of ℝ^d with finite Lebesgue measure. In this article we consider the quantity H(t)=∫_Ω ℙ^x (X_t∈Ω^c) dx which is called the heat content. We study its asymptotic expansion for isotropic α-stable Lévy processes and more general Lévy processes, under mild assumptions on the characteristic exponent.

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