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 and in a typical environment, at a distance larger than () from its initial position, is .
Mots clés : random walk in random environment, Sinai’s regime, $t$-stable point, moderate deviations
@article{PS_2004__8__56_0, author = {Comets, Francis and Popov, Serguei}, title = {A note on quenched moderate deviations for {Sinai's} random walk in random environment}, journal = {ESAIM: Probability and Statistics}, pages = {56--65}, publisher = {EDP-Sciences}, volume = {8}, year = {2004}, doi = {10.1051/ps:2004001}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2004001/} }
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 PY - 2004 SP - 56 EP - 65 VL - 8 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2004001/ DO - 10.1051/ps:2004001 LA - en ID - PS_2004__8__56_0 ER -
%0 Journal Article %A Comets, Francis %A Popov, Serguei %T A note on quenched moderate deviations for Sinai's random walk in random environment %J ESAIM: Probability and Statistics %D 2004 %P 56-65 %V 8 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps:2004001/ %R 10.1051/ps:2004001 %G en %F PS_2004__8__56_0
Comets, Francis; Popov, Serguei. A note on quenched moderate deviations for Sinai's random walk in random environment. ESAIM: Probability and Statistics, Tome 8 (2004), pp. 56-65. doi : 10.1051/ps:2004001. http://www.numdam.org/articles/10.1051/ps:2004001/
[1] Limit law for transition probabilities and moderate deviations for Sinai's random walk in random environment. Probab. Theory Relat. Fields 126 (2003) 571-609. | Zbl
and ,[2] Large deviations for a random walk in random environment. Ann. Probab. 22 (1994) 1381-1428. | MR | Zbl
and ,[3] The limits of Sinai's simple random walk in random environment. Ann. Probab. 26 (1998) 1477-1521. | Zbl
and ,[4] Moderate deviations for diffusions with Brownian potentials. (2003) Preprint PMA-792 available at http://www.proba.jussieu.fr/mathdoc/preprints/index.html#2003 | Zbl
and ,[5] Random Walks and Random Environments. Vol. 2. Random Environments. The Clarendon Press, Oxford University Press, New York (1996). | MR | Zbl
,[6] 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). | Zbl
,[7] Probability. 2nd edn., Springer, New York (1989). | MR | Zbl
,[8] The limiting behavior of one-dimensional random walk in random medium. Theory Probab. Appl. 27 (1982) 256-268. | MR | Zbl
,[9] Lecture Notes on Random Walks in Random Environment. (2003) Preliminary version at http://www-ee.technion.ac.il/~zeitouni/ps/notes1.ps | MR
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