# The exit path of a Markov chain with rare transitions

ESAIM: Probability and Statistics (2010)

- Volume: 1, page 95-144
- ISSN: 1292-8100

## Access Full Article

top## Abstract

top## How to cite

topCatoni, Olivier, and Cerf, Raphaël. "The exit path of a Markov chain with rare transitions." ESAIM: Probability and Statistics 1 (2010): 95-144. <http://eudml.org/doc/197768>.

@article{Catoni2010,

abstract = {
We study the exit path from a general domain after the last visit
to a set of a Markov chain with rare transitions. We prove several
large deviation principles for the law of the succession of the
cycles visited by the process (the cycle path), the succession of
the saddle points gone through to jump from cycle to cycle on the
cycle path (the saddle path) and the succession of all the points
gone through (the exit path). We estimate the time the process
spends in each cycle of the cycle path and how it decomposes into
the time spent in each point of the exit path. We describe a
systematic method to find the most likely saddle paths. We apply
these results to the reversible case of the Metropolis dynamics.
We give in appendix the corresponding large deviation estimates
in the non homogeneous case, which are corollaries of already
published works by Catoni (1992) and Trouvé (1992, 1996a).
},

author = {Catoni, Olivier, Cerf, Raphaël},

journal = {ESAIM: Probability and Statistics},

keywords = {Freidlin-Wentzell theory / large deviations /
exit / metastability.; Freidlin-Wentzell theory; large deviation principles; Metropolis dynamics; large deviation estimates},

language = {eng},

month = {3},

pages = {95-144},

publisher = {EDP Sciences},

title = {The exit path of a Markov chain with rare transitions},

url = {http://eudml.org/doc/197768},

volume = {1},

year = {2010},

}

TY - JOUR

AU - Catoni, Olivier

AU - Cerf, Raphaël

TI - The exit path of a Markov chain with rare transitions

JO - ESAIM: Probability and Statistics

DA - 2010/3//

PB - EDP Sciences

VL - 1

SP - 95

EP - 144

AB -
We study the exit path from a general domain after the last visit
to a set of a Markov chain with rare transitions. We prove several
large deviation principles for the law of the succession of the
cycles visited by the process (the cycle path), the succession of
the saddle points gone through to jump from cycle to cycle on the
cycle path (the saddle path) and the succession of all the points
gone through (the exit path). We estimate the time the process
spends in each cycle of the cycle path and how it decomposes into
the time spent in each point of the exit path. We describe a
systematic method to find the most likely saddle paths. We apply
these results to the reversible case of the Metropolis dynamics.
We give in appendix the corresponding large deviation estimates
in the non homogeneous case, which are corollaries of already
published works by Catoni (1992) and Trouvé (1992, 1996a).

LA - eng

KW - Freidlin-Wentzell theory / large deviations /
exit / metastability.; Freidlin-Wentzell theory; large deviation principles; Metropolis dynamics; large deviation estimates

UR - http://eudml.org/doc/197768

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.