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 -
