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2022 Large-time and small-time behaviors of the spectral heat content for time-changed stable processes
Kei Kobayashi, Hyunchul Park
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Electron. Commun. Probab. 27: 1-11 (2022). DOI: 10.1214/22-ECP478

Abstract

We study the large-time and small-time asymptotic behaviors of the spectral heat content for time-changed stable processes, where the time change belongs to a large class of inverse subordinators. For the large-time behavior, the spectral heat content decays polynomially with the decay rate determined by the Laplace exponent of the underlying subordinator, which is in sharp contrast to the exponential decay observed in the case when the time change is a subordinator. On the other hand, the small-time behavior exhibits three different decay regimes, where the decay rate is determined by both the Laplace exponent and the index of the stable process.

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Kei Kobayashi. Hyunchul Park. "Large-time and small-time behaviors of the spectral heat content for time-changed stable processes." Electron. Commun. Probab. 27 1 - 11, 2022. https://doi.org/10.1214/22-ECP478

Information

Received: 17 May 2022; Accepted: 25 July 2022; Published: 2022
First available in Project Euclid: 22 August 2022

Digital Object Identifier: 10.1214/22-ECP478

Subjects:
Primary: 60G51 , 60K50

Keywords: inverse subordinator , spectral heat content , time-changed stable process

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