Green function for Schrödinger operator and conditioned Feynman-Kac gauge

Conditional gauge theorem for non - local Feynman - Kac transforms

Feynman-Kac transforms driven by discontinuous additive functionals are studied in this paper for a large class of Markov processes. General gauge and conditional gauge theorems are established for such transforms. Furthermore, the L2-infinitesimal generator of the Schrödinger semigroup given by a non-local Feynman-Kac transform is determined in terms of its associated bilinear form.

A Feynman-Kac path-integral implementation for Poisson's equation using an h-conditioned Green's function

This study presents a Feynman–Kac path-integral implementation for solving the Dirichlet problem for Poisson’s equation. The algorithm is a modified “walk on spheres” (WOS) that includes the Feynman–Kac path-integral contribution for the source term. In our approach, we use an h-conditioned Green’s function instead of simulating Brownian trajectories in detail to implement this path-integral co...

An Operator Bound Related to Feynman-kac Formulae

Those Fourier matrix multiplier operators which are convolutions with respect to a matrix valued measure are characterised in terms of an operator bound. As an application, the finite-dimensional distributions of the process associated with Dirac equation are shown to be unbounded on the algebra of cylinder sets. In its traditional incarnation, the Feynman-Kac formula is a means of expressing a...

The Feynman-kac Formula in the Operator Setting

Quantum Feynman-Kac perturbations