Variational processes and stochastic versions of mechanics
- 1 September 1986
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 27 (9), 2307-2330
- https://doi.org/10.1063/1.527002
Abstract
The dynamical structure of any reasonable stochastic version of classical mechanics is investigated, including the version created by Nelson [E. Nelson, Quantum Fluctuations (Princeton U.P., Princeton, NJ, 1985); Phys. Rev. 150, 1079 (1966)] for the description of quantum phenomena. Two different theories result from this common structure. One of them is the imaginary time version of Nelson’s theory, whose existence was unknown, and yields a radically new probabilistic interpretation of the heat equation. The existence and uniqueness of all the involved stochastic processes is shown under conditions suggested by the variational approach of Yasue [K. Yasue, J. Math. Phys. 22, 1010 (1981)].This publication has 12 references indexed in Scilit:
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