The exit path of a Markov chain with rare transitions

Catoni, 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 -