Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space

Matthias Albrecht Fahrenwaldt

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Abstract

We derive the heat trace asymptotics of the generator of subordinate Brownian motion on Euclidean space for a class of Laplace exponents. The terms in the asymptotic expansion can be computed to arbitrary order and depend both on the geometry of Euclidean space and the short-time behaviour of the process. If the Blumenthal-Getoor index of the process is rational, then the asymptotics may contain logarithmic terms. The key assumption is the existence of a suitable density for the Lévy measure of the subordinator. The analysis is highly explicit.
Original languageEnglish
Pages (from-to)331-354
Number of pages24
JournalPotential Analysis
Volume44
Issue number2
Early online date24 Oct 2015
DOIs
Publication statusPublished - Feb 2016

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