First Order Feynman-Kac Formula

TL;DR

This paper derives formulas and estimates for Feynman-Kac kernels and their derivatives on manifolds with a pole, using Gaussian and semi-classical bridge approaches under Riemannian assumptions.

Contribution

It introduces new formulas and estimates for Feynman-Kac kernels on manifolds with a pole, expanding understanding of their behavior and derivatives.

Findings

Formulas for Feynman-Kac kernels and derivatives on manifolds with a pole.

Estimates involving Gaussian terms and semi-classical bridges.

Results depend on specific Riemannian geometric assumptions.

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.