A unified approach to the small-time behavior of the spectral heat content for isotropic Lévy processes

Kei Kobayashi and Hyunchul Park

Stochastic Processes and their Applications, 2024, vol. 171, issue C

Abstract: This paper establishes the precise small-time asymptotic behavior of the spectral heat content for isotropic Lévy processes on bounded C1,1 open sets of Rd with d≥2, where the underlying characteristic exponents are regularly varying at infinity with index α∈(1,2], including the case α=2. Moreover, this asymptotic behavior is shown to be stable under an integrable perturbation of its Lévy measure. These results cover a wide class of isotropic Lévy processes, including Brownian motions, stable processes, and jump diffusions, and the proofs provide a unified approach to the asymptotic behavior of the spectral heat content for all of these processes.

Keywords: Spectral heat content; Isotropic Lévy process; Asymptotic behavior (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2024.104331

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