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.
Publié le : 1997-04-14
Classification:
Schrödinger processes,
Brownian motion,
Brownian sheet,
space-time harmonic functions,
relative entropy,
entropy minimization under given marginals,
large deviations,
stochastic mechanics,
60J65,
60F10,
60J45,
60J25,
94A17
@article{1024404423,
author = {F\"ollmer, Hans and Gantert, Nina},
title = {Entropy minimization and Schr\"odinger processes in infinite
dimensions},
journal = {Ann. Probab.},
volume = {25},
number = {4},
year = {1997},
pages = { 901-926},
language = {en},
url = {http://dml.mathdoc.fr/item/1024404423}
}
Föllmer, Hans; Gantert, Nina. Entropy minimization and Schrödinger processes in infinite
dimensions. Ann. Probab., Tome 25 (1997) no. 4, pp. 901-926. http://gdmltest.u-ga.fr/item/1024404423/