A Gibson approach to infinite-dimensional Brownian diffusions (Q1908542)
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scientific article; zbMATH DE number 849092
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Gibson approach to infinite-dimensional Brownian diffusions |
scientific article; zbMATH DE number 849092 |
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A Gibson approach to infinite-dimensional Brownian diffusions (English)
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31 March 1996
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We establish a one-to-one correspondence between the laws of smooth infinite-dimensional Brownian diffusions and the Gibbs states on the path space \(\Omega = C(0,1)^{\mathbb{Z}^d}\). Applications to phase transition, time reversal and reversible measures are then discussed. The main tool is a characterization of Gibbs states via an infinite-dimensional version of the Malliavin calculus integration.
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Brownian diffusions
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Gibbs states
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Malliavin calculus
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