A Feynman-Kac-type formula for the deterministic and stochastic wave equations

Robert C. Dalang; Carl Mueller; Roger Tribe

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arXiv · 0710.2861

A Feynman-Kac-type formula for the deterministic and stochastic wave equations

Robert C. Dalang·Carl Mueller·Roger Tribe

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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.

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Robert C. Dalang, Carl Mueller, Roger Tribe. 2007-10-15. A Feynman-Kac-type formula for the deterministic and stochastic wave equations. https://arxiv.org/abs/0710.2861

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