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Zbl 0864.60001
Zambrini, Jean-Claude
Feynman and the mathematics. (Feynman et les mathématiques.) (French)
[J] Ann. Math. Blaise Pascal 3, No.1, 211-226 (1996). ISSN 1259-1734

Summary: We summarize a probabilistic version, inspired by E. Schrödinger, of Feynman's quantization method for elementary classical systems via path integrals. This suggests new perspectives for the study of Hamilton-Jacobi-Bellman equation. In particular, the use of some probabilistic conservation laws should allow us to solve it, as Jacobi was able to integrate (by ``quadrature'') some classical equations of motion.

MSC 2000:: *60A99 Foundations of probability theory
81Q30 Feynman integrals and graphs

Keywords: quantization method for elementary classical systems via path integrals; probabilistic conservation laws

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