### Abstract

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 | |

State | Published - Feb 2016 |

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### Cite this

*Potential Analysis*,

*44*(2), 331-354. DOI: 10.1007/s11118-015-9514-1

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*Potential Analysis*, vol 44, no. 2, pp. 331-354. DOI: 10.1007/s11118-015-9514-1

**Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space.** / Fahrenwaldt, Matthias Albrecht.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Heat Trace Asymptotics of Subordinate Brownian Motion in Euclidean Space

AU - Fahrenwaldt,Matthias Albrecht

PY - 2016/2

Y1 - 2016/2

N2 - 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.

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.

U2 - 10.1007/s11118-015-9514-1

DO - 10.1007/s11118-015-9514-1

M3 - Article

VL - 44

SP - 331

EP - 354

JO - Potential Analysis

T2 - Potential Analysis

JF - Potential Analysis

SN - 0926-2601

IS - 2

ER -