Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages331-354
Number of pages24
JournalPotential Analysis
Volume44
Issue number2
Early online date24 Oct 2015
DOIs
StatePublished - Feb 2016

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Brownian motion
Euclidean space
Heat
Trace
Subordinator
Lévy Measure
Term
Laplace
Asymptotic Expansion
Logarithmic
Exponent
Generator
Arbitrary
Class

Cite this

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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 L\{'e}vy measure of the subordinator. The analysis is highly explicit.",
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Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space. / Fahrenwaldt, Matthias Albrecht.

In: Potential Analysis, Vol. 44, No. 2, 02.2016, p. 331-354.

Research output: Contribution to journalArticle

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