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

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

2007-10-15

arxiv.org/abs/0710.2861v1

Trans. Amer. Math. Soc. 360, 4681-4703, (2008)

Mathematics

Probability

To appear in TAMS

Scientific paper

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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