In this note, we use the Feynman-Kac formula to derive a moment representation for the 2D parabolic Anderson model in small time, which is related to the intersection local time of planar Brownian motions.

In a reasonably self-contained and explicit presentation we illustrate the efficiency of the Feynman–Kac formula for the rigorous derivation of three inequalities of interest in non-relativistic quantum mechanics.

In this paper, we present numerical methods to implement the probabilistic representation of third kind (Robin) boundary problem for the Laplace equations. The solution is based on a Feynman–Kac formula for the Robin problem which employs the standard reflecting Brownian motion (SRBM) and its boundary local time arising from the Skorokhod problem. By simulating SRBM paths through Brownian motio...

We propose an algorithm based on variational quantum imaginary time evolution for solving the Feynman-Kac partial differential equation resulting from a multidimensional system of stochastic equations. utilize correspondence between (PDE) and Wick-rotated Schr\"{o}dinger this purpose. The results $(2+1)$ dimensional obtained through are then compared against classical ODE solvers Monte Carlo si...