First Order Feynman-Kac Formula

2016/08/12 by Xue-Mei Li, James Thompson, Li, Xue-Mei +1
Mathematics · #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Probability (math.PR) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1608.03856

openalex publication_date 2016/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the parabolic integral kernel associated with the weighted Laplacian and the Feynman-Kac kernels. For manifold with a pole we deduce formulas and estimates for them and for their derivatives, given in terms of a Gaussian term and the semi-classical bridge. Assumptions are on the Riemannian data.

Citations

• On the parabolic kernel of the Schrödinger operator
• Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
• Hessian formulas and estimates for parabolic Schrödinger operators
• Generalised Brownian bridges: examples

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