Feynman–Kac formula

The Feynman–Kac formula, named after Richard Feynman and Mark Kac, establishes a link between parabolic partial differential equations and stochastic processes. In 1947, when Kac and Feynman were both faculty members at Cornell University, Kac attended a presentation of Feynman's and remarked that the two of them were working on the same thing from different directions. The Feynman–Kac formula resulted, which proves rigorously a real-valued analogy to Feynman's path integrals. The complex case, needed in quantum mechanics, is still an open question.

The formula offers a method of solving certain partial differential equations by simulating random paths of a stochastic process. Conversely, it can be used to compute an important class of expectations of random processes by deterministic means.

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