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Uniform Asymptotic Bounds for the Heat Kernel and the Trace of a Stochastic Geodesic Flow
University of Bonn, Institute of Applied Mathematics.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
University of Warwick, Department of Statistics.
2012 (English)In: Stochastics: An International Journal of Probablitiy and Stochastic Processes, ISSN 1744-2508, E-ISSN 1744-2516, Vol. 84, no 2-3, p. 315-333Article in journal (Refereed) Published
Abstract [en]

We analyze the asymptotic behaviour of the heat kernel dened by a stochastically perturbedgeodesic ow on the cotangent bundle of a Riemannian manifold for small time and smalldiusion parameter. This extends WKB-type methods to a particular case of a degenerateHamiltonian. We give uniform bounds for the solution of the degenerate Hamiltonian boundaryvalue problem for small time. The results are exploited to derive two sided estimates andmultiplicative asymptotics for the heat kernel semigroup and its trace.

Place, publisher, year, edition, pages
2012. Vol. 84, no 2-3, p. 315-333
Keywords [en]
Asymptotic expansions, heat kernel, stochastic geodesic ow, trace formula
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-7705DOI: 10.1080/17442508.2010.519029ISI: 000303571000013Scopus ID: 2-s2.0-84860329759OAI: oai:DiVA.org:lnu-7705DiVA, id: diva2:345078
Conference
International Conference on Stochastic Analysis and Applications Location: Hammamet, TUNISIA Date: OCT 12-17, 2009
Note

Online first 09 Jun 2011

Available from: 2010-08-23 Created: 2010-08-23 Last updated: 2017-12-12Bibliographically approved

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Hilbert, Astrid

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  • en-US
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  • nn-NO
  • nn-NB
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