(Homogeneous) markovian bridges

Vincent Vigon

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 3, page 875-916
  • ISSN: 0246-0203

Abstract

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(Homogeneous) Markov bridges are (time homogeneous) Markov chains which begin at a given point and end at a given point. The price to pay for preserving the homogeneity is to work with processes with a random life-span. Bridges are studied both for themselves and for their use in describing the transformations of Markov chains: restriction on a random interval, time reversal, time change, various conditionings comprising the confinement in some part of the state space. These bridges lead us to look at Markov chains from an unusual point of view: we will work, no longer with only one transition matrix, but with a class of matrices which can be deduced one from the other by Doob transformations. This way of proceeding has the advantage of better describing the “past ↔ future symmetries”: The symmetry of conditional independence (well known) and the symmetry of homogeneity (less well known).

How to cite

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Vigon, Vincent. "(Homogeneous) markovian bridges." Annales de l'I.H.P. Probabilités et statistiques 47.3 (2011): 875-916. <http://eudml.org/doc/242908>.

@article{Vigon2011,
abstract = {(Homogeneous) Markov bridges are (time homogeneous) Markov chains which begin at a given point and end at a given point. The price to pay for preserving the homogeneity is to work with processes with a random life-span. Bridges are studied both for themselves and for their use in describing the transformations of Markov chains: restriction on a random interval, time reversal, time change, various conditionings comprising the confinement in some part of the state space. These bridges lead us to look at Markov chains from an unusual point of view: we will work, no longer with only one transition matrix, but with a class of matrices which can be deduced one from the other by Doob transformations. This way of proceeding has the advantage of better describing the “past ↔ future symmetries”: The symmetry of conditional independence (well known) and the symmetry of homogeneity (less well known).},
author = {Vigon, Vincent},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Markov chains; random walks; LU-factorization; path-decomposition; fluctuation theory; probabilistic potential theory; infinite matrices; Martin boundary; Markov bridges; Wiener-Hopf factorization},
language = {eng},
number = {3},
pages = {875-916},
publisher = {Gauthier-Villars},
title = {(Homogeneous) markovian bridges},
url = {http://eudml.org/doc/242908},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Vigon, Vincent
TI - (Homogeneous) markovian bridges
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 3
SP - 875
EP - 916
AB - (Homogeneous) Markov bridges are (time homogeneous) Markov chains which begin at a given point and end at a given point. The price to pay for preserving the homogeneity is to work with processes with a random life-span. Bridges are studied both for themselves and for their use in describing the transformations of Markov chains: restriction on a random interval, time reversal, time change, various conditionings comprising the confinement in some part of the state space. These bridges lead us to look at Markov chains from an unusual point of view: we will work, no longer with only one transition matrix, but with a class of matrices which can be deduced one from the other by Doob transformations. This way of proceeding has the advantage of better describing the “past ↔ future symmetries”: The symmetry of conditional independence (well known) and the symmetry of homogeneity (less well known).
LA - eng
KW - Markov chains; random walks; LU-factorization; path-decomposition; fluctuation theory; probabilistic potential theory; infinite matrices; Martin boundary; Markov bridges; Wiener-Hopf factorization
UR - http://eudml.org/doc/242908
ER -

References

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