Entropy minimization and Schrödinger processes in infinite dimensions
type: Item
instance of: scholarly article
title: Entropy minimization and Schrödinger processes in infinite dimensions
zbMATH Open document ID: 0876.60063
author: Hans Föllmer
author: Nina Gantert
published in: The Annals of Probability
publication date: 1997-11-10T00:00:00Z
review text: A Schrödinger process is a Markov process that can be expressed as a mixture of Brownian bridges. In finite-dimensional spaces, they appear in a problem of large deviation involving minimization of the relative entropy with fixed marginals, which has been considered first by Schrödinger, and can also be obtained as a Doob's \(h\)-transform of Brownian motion for a certain class of space-time harmonic functions. The paper investigates the analogous connections in infinite dimension.
reviewed by: Jean Bertoin
Mathematics Subject Classification ID: 60J65
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60J45
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 1018413
zbMATH Keywords: Schrödinger process
zbMATH Keywords: Brownian bridges
zbMATH Keywords: large deviation
zbMATH Keywords: space-time harmonic functions
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1024404423
OpenAlex ID: W2051326392
cites work: Q4872453
cites work: Q4752882
cites work: An automorphism of product measures
cites work: Decomposition of Multivariate Functions
cites work: Entropy minimization, \(DAD\) problems, and doubly stochastic kernels
cites work: Q4870543
cites work: I-divergence geometry of probability distributions and minimization problems
cites work: Schrödinger processes and large deviations
cites work: Asymptotic evaluation of certain markov process expectations for large time, II
cites work: Q3342857
cites work: Q3810626
cites work: Résolution d'un système d'équations de M. Schrödinger
cites work: Self-similarity of Brownian motion and a large deviation principle for random fields on a binary tree
cites work: Reciprocal processes
cites work: The Markov processes of Schr�dinger
cites work: Note on the Schrödinger equation and \(I\)-projections
cites work: Q4482179
cites work: Second order stochastic differential equations and non-Gaussian reciprocal diffusions
cites work: Symmetries in the stochastic calculus of variations
DOI: 10.1214/AOP/1024404423
description: scientific article; zbMATH DE number 1018413