Wiener measures on Riemannian manifolds and the Feynman-Kac formula

  • This is an introduction to Wiener measure and the Feynman-Kac formula on general Riemannian manifolds for Riemannian geometers with little or no background in stochastics. We explain the construction of Wiener measure based on the heat kernel in full detail and we prove the Feynman-Kac formula for Schrödinger operators with bounded potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.

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Metadaten
Author:Christian Bär, Frank Pfäffle
URN:urn:nbn:de:kobv:517-opus-59998
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 (1(2012)17)
Document Type:Preprint
Language:English
Date of Publication (online):2012/07/05
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/07/05
Tag:Brownian bridge; Brownian motion; Riemannian manifold; Wiener measure; conditional Wiener measure
Source:arXiv:1108.5082v1 [math.DG] 25 Aug 2011
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J35 Heat and other parabolic equation methods
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J65 Diffusion processes and stochastic analysis on manifolds [See also 35R60, 60H10, 60J60]
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990