Blog
About

  • Record: found
  • Abstract: found
  • Article: found
Is Open Access

Wiener Measures on Riemannian Manifolds and the Feynman-Kac Formula

Preprint

Read this article at

Bookmark
      There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.

      Abstract

      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 Schr\"odinger operators with \(L^\infty\)-potentials. We also consider normal Riemannian coverings and show that projecting and lifting of paths are inverse operations which respect the Wiener measure.

      Related collections

      Author and article information

      Journal
      2011-08-25
      2012-07-17
      1108.5082

      http://arxiv.org/licenses/nonexclusive-distrib/1.0/

      Custom metadata
      58J65, 58J35
      Matematica Contemporanea 40 (2011), 37-90
      reference added, a few minor changes, published version
      math.DG math.PR

      Probability, Geometry & Topology

      Comments

      Comment on this article