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April 1997 Entropy minimization and Schrödinger processes in infinite dimensions
Hans Föllmer, Nina Gantert
Ann. Probab. 25(2): 901-926 (April 1997). DOI: 10.1214/aop/1024404423


Schrödinger 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 Schrödinger which involves minimization of relative entropy with given marginals. As a basic case study in infinite dimensions, we investigate these different aspects for Schrödinger processes of infinite-dimensional Brownian motion. The results and examples concerning entropy minimization with given marginals are of independent interest.


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Hans Föllmer. Nina Gantert. "Entropy minimization and Schrödinger processes in infinite dimensions." Ann. Probab. 25 (2) 901 - 926, April 1997.


Published: April 1997
First available in Project Euclid: 18 June 2002

zbMATH: 0876.60063
MathSciNet: MR1434130
Digital Object Identifier: 10.1214/aop/1024404423

Primary: 60F10 , 60J25 , 60J45 , 60J65 , 94A17

Keywords: Brownian motion , Brownian sheet , entropy minimization under given marginals , large deviations , Relative entropy , Schrödinger processes , space-time harmonic functions , stochastic mechanics

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.25 • No. 2 • April 1997
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