Malliavin calculus and euclidean quantum mechanics II. Variational principle for infinite dimensional processes

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Abstract

A class of time reversible non-stationary diffusion processes with values on the classical Wiener space is constructed. These processes should be relevant to ("2-dimensional") Euclidean quantum field theory since they generalize those constructed before for non-relativistic quantum mechanics, along the lines of a strategy suggested by Schrödinger. Those processes are shown to be characterized by a stochastic variational principle and provide a probabilistic representation of the solutions of some infinite-dimensional heat equation. The Feynman-Kac formula on the Wiener space needed for this construction is also proved. © 1995 Academic Press Limited.

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Cruzeiro, A. B., & Zambrini, J. C. (1995). Malliavin calculus and euclidean quantum mechanics II. Variational principle for infinite dimensional processes. Journal of Functional Analysis, 130(2), 450–476. https://doi.org/10.1006/jfan.1995.1077

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