For strongly ergodic discrete time Markov chains we discuss the possible limits as n→∞ of probability measures on the path space of the form exp(nH(Ln)) dP/Zn· Ln is the empirical measure (or sojourn measure) of the process, H is a real-valued function (possibly attaining −∞) on the space of probability measures on the state space of the chain, and Zn is the appropriate norming constant. The class of these transformations also includes conditional laws given Ln belongs to some set. The possible limit laws are mixtures of Markov chains minimizing a certain free energy. The method of proof strongly relies on large deviation techniques.

Bolthausen, E; Schmock, U (1989). *On the maximum entropy principle for uniformly ergodic Markov chains.* Stochastic Processes and their Applications, 33(1):1-27.

## Abstract

For strongly ergodic discrete time Markov chains we discuss the possible limits as n→∞ of probability measures on the path space of the form exp(nH(Ln)) dP/Zn· Ln is the empirical measure (or sojourn measure) of the process, H is a real-valued function (possibly attaining −∞) on the space of probability measures on the state space of the chain, and Zn is the appropriate norming constant. The class of these transformations also includes conditional laws given Ln belongs to some set. The possible limit laws are mixtures of Markov chains minimizing a certain free energy. The method of proof strongly relies on large deviation techniques.

## Citations

## Altmetrics

## Additional indexing

Item Type: | Journal Article, refereed, original work |
---|---|

Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Uncontrolled Keywords: | maximum entropy; large deviations; Markov chains; variational problem; weak convergence |

Language: | English |

Date: | 1989 |

Deposited On: | 04 Nov 2009 14:31 |

Last Modified: | 05 Apr 2016 13:29 |

Publisher: | Elsevier |

ISSN: | 0304-4149 |

Publisher DOI: | 10.1016/0304-4149(89)90063-X |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1027105 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0691.60023 |

## Download

Full text not available from this repository.View at publisher

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.

You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.