On computer simulation of Feynman-Kac path-integrals

On the approximation of Feynman-Kac path integrals

The symbol D [x (τ)] indicates that the integration is performed over the set of all differentiable curves, x : [0, βh̄]→ R, with x (0) = a and x (βh̄) = b. The integer d reflects the dimensionality, with d = 3N for a system of N -particles in 3-dimensional space. The functional Φ can be derived from the classical action by introducing a relationship between temperature and imaginary time (it = β...

Perfect simulation for the Feynman-Kac law on the path space

This paper describes an algorithm of interest. This is a preliminary version and we intend on writing a better descripition of it and getting bounds for its complexity.

Feynman path integrals on phase space and the metaplectic representation

A Feynman-Kac Path-Integral Implementation for Poisson's Equation

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 FeynmanKac path-integral contribution for the source term. In our approach, we use the Poisson kernel instead of simulating Brownian trajectories in detail to implement the path-integral computation. We der...

Quantum Feynman-Kac perturbations