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Derivatives of Feynman–Kac Semigroups

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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.

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Authors and Affiliations

  1. Mathematics Research Unit, University of Luxembourg, Esch-sur-Alzette, Luxembourg

    James Thompson

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  1. James Thompson
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Correspondence to James Thompson.

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James Thompson is supported by the Fonds National de la Recherche Luxembourg (OPEN Project GEOMREV).

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Thompson, J. Derivatives of Feynman–Kac Semigroups. J Theor Probab 32, 950–973 (2019). https://doi.org/10.1007/s10959-018-0824-2

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  • DOI: https://doi.org/10.1007/s10959-018-0824-2

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