Malliavin Calculus and Euclidean Quantum Mechanics II. Variational Principle for Infinite Dimensional Processes
✍ Scribed by A.B. Cruzeiro; J.C. Zambrini
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 826 KB
- Volume
- 130
- Category
- Article
- ISSN
- 0022-1236
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✦ Synopsis
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. Inc.