Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space

Matthias Albrecht Fahrenwaldt

doi:10.1007/s11118-015-9514-1

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 language	English
Pages (from-to)	331-354
Number of pages	24
Journal	Potential Analysis
Volume	44
Issue number	2
Early online date	24 Oct 2015
DOIs	https://doi.org/10.1007/s11118-015-9514-1
Publication status	Published - Feb 2016

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title = "Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space",

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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AB - 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.

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JO - Potential Analysis

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Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space

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