A Feynman-Kac-type formula for the deterministic and stochastic wave equations
Probability
2011-02-18 v1
Abstract
We establish a probabilistic representation for a wide class of linear deterministic p.d.e.s with potential term, including the wave equation in spatial dimensions 1 to 3. Our representation applies to the heat equation, where it is related to the classical Feynman-Kac formula, as well as to the telegraph and beam equations. If the potential is a (random) spatially homogeneous Gaussian noise, then this formula leads to an expression for the moments of the solution.
Cite
@article{arxiv.0710.2861,
title = {A Feynman-Kac-type formula for the deterministic and stochastic wave equations},
author = {Robert C. Dalang and Carl Mueller and Roger Tribe},
journal= {arXiv preprint arXiv:0710.2861},
year = {2011}
}
Comments
To appear in TAMS