The Annals of Probability

Entropy minimization and Schrödinger processes in infinite dimensions

Hans Föllmer and Nina Gantert

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Abstract

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.

Article information

Source
Ann. Probab., Volume 25, Number 2 (1997), 901-926.

Dates
First available in Project Euclid: 18 June 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1024404423

Digital Object Identifier
doi:10.1214/aop/1024404423

Mathematical Reviews number (MathSciNet)
MR1434130

Zentralblatt MATH identifier
0876.60063

Subjects
Primary: 60J65: Brownian motion [See also 58J65] 60F10: Large deviations 60J45: Probabilistic potential theory [See also 31Cxx, 31D05] 60J25: Continuous-time Markov processes on general state spaces 94A17: Measures of information, entropy

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

Citation

Föllmer, Hans; Gantert, Nina. Entropy minimization and Schrödinger processes in infinite dimensions. Ann. Probab. 25 (1997), no. 2, 901--926. doi:10.1214/aop/1024404423. https://projecteuclid.org/euclid.aop/1024404423


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