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Journal of Theoretical Probability

, Volume 32, Issue 2, pp 950–973 | Cite as

Derivatives of Feynman–Kac Semigroups

  • James ThompsonEmail author
Article
  • 38 Downloads

Abstract

We prove Bismut-type formulae for the first and second derivatives of a Feynman–Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, although the assumptions are purely geometric.

Keywords

Brownian motion Feynman–Kac Bismut 

Mathematics Subject Classification (2010)

47D08 53B20 58J65 60J65 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mathematics Research UnitUniversity of LuxembourgEsch-sur-AlzetteLuxembourg

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