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Entropy Minimization and Schrodinger Processes in Infinite Dimensions

Hans Follmer and Nina Gantert
The Annals of Probability
Vol. 25, No. 2 (Apr., 1997), pp. 901-926
Stable URL: http://www.jstor.org/stable/2959615
Page Count: 26
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Entropy Minimization and Schrodinger Processes in Infinite Dimensions
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Abstract

Schrodinger processes are defined as mixtures of Brownian bridges which preserve the Markov property. In finite dimensions, they can be characterized as h-transforms in the sense of Doob for some space-time harmonic function h of Brownian motion, and also as solutions to a large deviation problem introduced by Schrodinger which involves minimization of relative entropy with given marginals. As a basic case study in infinite dimensions, we investigate these different aspects for Schrodinger processes of infinite-dimensional Brownian motion. The results and examples concerning entropy minimization with given marginals are of independent interest.

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