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First order Feynman–Kac formula

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  • Li, Xue-Mei
  • Thompson, James

Abstract

We study the parabolic integral kernel for the weighted Laplacian with a potential. For manifolds with a pole we deduce formulas and estimates for the derivatives of the Feynman–Kac kernels and their logarithms, these are in terms of a ‘Gaussian’ term and the semi-classical bridge.

Suggested Citation

  • Li, Xue-Mei & Thompson, James, 2018. "First order Feynman–Kac formula," Stochastic Processes and their Applications, Elsevier, vol. 128(9), pages 3006-3029.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:9:p:3006-3029
    DOI: 10.1016/j.spa.2017.10.010
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    References listed on IDEAS

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    1. Li, Xiang-Dong, 2016. "Hamilton’s Harnack inequality and the W-entropy formula on complete Riemannian manifolds," Stochastic Processes and their Applications, Elsevier, vol. 126(4), pages 1264-1283.
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    Cited by:

    1. James Thompson, 2020. "Functional Inequalities for Feynman–Kac Semigroups," Journal of Theoretical Probability, Springer, vol. 33(3), pages 1523-1540, September.

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