Some pointers to the (extensive) literature on generalized Feyman-Kac formulas:
- Stochastic Solution of Elliptic and Parabolic Boundary Value Problems for the Spectral Fractional Laplacian
- Fractional Feynman-Kac Equation for Non-Brownian Functionals
- The Feynman–Kac formula for Schrödinger operators on vector bundles over complete manifolds