A note on quenched moderate deviations for Sinai's random walk in random environment
ESAIM: Probability and Statistics (2010)
- Volume: 8, page 56-65
- ISSN: 1292-8100
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topComets, Francis, and Popov, Serguei. "A note on quenched moderate deviations for Sinai's random walk in random environment." ESAIM: Probability and Statistics 8 (2010): 56-65. <http://eudml.org/doc/104322>.
@article{Comets2010,
abstract = {
We consider the continuous time,
one-dimensional random walk in random environment
in Sinai's regime. We show that the probability for the
particle to be, at time t and in a typical environment,
at a distance larger than ta (0<a<1)
from its initial position, is exp\{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))\}.
},
author = {Comets, Francis, Popov, Serguei},
journal = {ESAIM: Probability and Statistics},
keywords = {Random walk in random environment; Sinai's regime; t-stable point; moderate deviations.; -stable point; moderate deviations},
language = {eng},
month = {3},
pages = {56-65},
publisher = {EDP Sciences},
title = {A note on quenched moderate deviations for Sinai's random walk in random environment},
url = {http://eudml.org/doc/104322},
volume = {8},
year = {2010},
}
TY - JOUR
AU - Comets, Francis
AU - Popov, Serguei
TI - A note on quenched moderate deviations for Sinai's random walk in random environment
JO - ESAIM: Probability and Statistics
DA - 2010/3//
PB - EDP Sciences
VL - 8
SP - 56
EP - 65
AB -
We consider the continuous time,
one-dimensional random walk in random environment
in Sinai's regime. We show that the probability for the
particle to be, at time t and in a typical environment,
at a distance larger than ta (0<a<1)
from its initial position, is exp{-Const ⋅ ta/[(1 - a)lnt](1 + o(1))}.
LA - eng
KW - Random walk in random environment; Sinai's regime; t-stable point; moderate deviations.; -stable point; moderate deviations
UR - http://eudml.org/doc/104322
ER -
References
top- F. Comets and S.Yu. Popov, Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment. Probab. Theory Relat. Fields 126 (2003) 571-609.
- A. Greven and F. den Hollander, Large deviations for a random walk in random environment. Ann. Probab.22 (1994) 1381-1428.
- Y. Hu and Z. Shi, The limits of Sinai's simple random walk in random environment. Ann. Probab.26 (1998) 1477-1521.
- Y. Hu and Z. Shi, Moderate deviations for diffusions with Brownian potentials. (2003) Preprint PMA–792 available at www.proba.jussieu.fr/mathdoc/preprints/index.html#2003
- B. Hughes, Random Walks and Random Environments. Vol. 2. Random Environments. The Clarendon Press, Oxford University Press, New York (1996).
- Z. Shi, Sinai's Walk via Stochastic Calculus, in Milieux Aléatoires, F. Comets and E. Pardoux Eds., Société Mathématique de France, Paris, Panoramas et Synthèses 12 (2001).
- A. Shiryaev, Probability. 2nd edn., Springer, New York (1989).
- Ya.G. Sinai, The limiting behavior of one-dimensional random walk in random medium. Theory Probab. Appl.27 (1982) 256-268.
- O. Zeitouni, Lecture Notes on Random Walks in Random Environment. (2003) Preliminary version at www-ee.technion.ac.il/~zeitouni/ps/notes1.ps
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