Malliavin Calculus and Euclidean Quantum Mechanics II. Variational Principle for Infinite Dimensional Processes
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 mechani...
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| Veröffentlicht in: | Journal of functional analysis 1995-06, Vol.130 (2), p.450-476 |
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| container_end_page | 476 |
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| container_issue | 2 |
| container_start_page | 450 |
| container_title | Journal of functional analysis |
| container_volume | 130 |
| creator | Cruzeiro, A.B. Zambrini, J.C. |
| description | 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. |
| doi_str_mv | 10.1006/jfan.1995.1077 |
| format | Article |
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| ispartof | Journal of functional analysis, 1995-06, Vol.130 (2), p.450-476 |
| issn | 0022-1236 1096-0783 |
| language | eng |
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| source | Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals |
| title | Malliavin Calculus and Euclidean Quantum Mechanics II. Variational Principle for Infinite Dimensional Processes |
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