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Bernstein processes associated with a Markov process. (English) Zbl 0965.60101

Rebolledo, Rolando (ed.), Stochastic analysis and mathematical physics. ANESTOC ’98, proceedings of the 3rd international workshop, Santiago, Chile, October 1998. Boston: Birkhäuser. 41-72 (2000).
Summary: A general description of Bernstein processes, a class of diffusion processes, relevant to the probabilistic counterpart of quantum theory known as Euclidean quantum mechanics, is given. It is compatible with finite- or infinite-dimensional state spaces and singular interactions. Although the relations with statistical physics concepts (Gibbs measure, entropy,\(\dots\)) is stressed here, recent developments requiring Feynman’s quantum mechanical tools (action functional, path integrals, Noether’s theorem, \(\dots)\) are also mentioned and suggest new research directions, especially in the geometrical structure of our approach.
For the entire collection see [Zbl 0942.00035].

MSC:

60K40 Other physical applications of random processes
81P20 Stochastic mechanics (including stochastic electrodynamics)
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