A law of large numbers for random walks in random environment

被引：125

作者：

Sznitman, AS ^{[1
]}

Zerner, MPW ^{[1
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, CH-8092 Zurich, Switzerland

来源：

ANNALS OF PROBABILITY | 1999年 / 27卷 / 04期

关键词：

random walk in random environment; law of large numbers; Kalikow's condition; renewal structure;

D O I：

10.1214/aop/1022874818

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We derive a law of large numbers for a class of multidimensional random walks in random environment satisfying a condition which first appeared in the work of Kalikow. The approach is based on the existence of a renewal structure under an assumption of "transience in the direction l." This extends, to a multidimensional context, previous work of Kesten. Our results also enable proving the convergence of the law of the environment viewed from the particle toward a limiting distribution.

引用

页码：1851 / 1869

页数：19

共 50 条

[1] A NON-BALLISTIC LAW OF LARGE NUMBERS FOR RANDOM WALKS IN IID RANDOM ENVIRONMENT
Zerner, Martin P. W.
[J]. ELECTRONIC COMMUNICATIONS IN PROBABILITY, 2002, 7 : 191 - 197
[2] The point of view of the particle on the law of large numbers for random walks in a mixing random environment
Rassoul-Agha, F
[J]. ANNALS OF PROBABILITY, 2003, 31 (03): : 1441 - 1463
[3] A law of large numbers for random walks in random mixing environments
Comets, F
Zeitouni, O
[J]. ANNALS OF PROBABILITY, 2004, 32 (1B): : 880 - 914
[4] Law of large numbers for a class of random walks in dynamic random environments
Avena, L.
Den Hollander, F.
Redig, F.
[J]. ELECTRONIC JOURNAL OF PROBABILITY, 2011, 16 : 587 - 617
[5] Dynamic Zd-random walks in a random scenery:: a strong law of large numbers
Guillotin-Plantard, N
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1999, 329 (08): : 711 - 716
[6] Law of large numbers for non-elliptic random walks in dynamic random environments
den Hollander, F.
dos Santos, R.
Sidoravicius, V.
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2013, 123 (01) : 156 - 190
[7] Dynamic ℤd-Random Walks in a Random Scenery: A Strong Law of Large Numbers
N. Guillotin-Plantard
[J]. Journal of Theoretical Probability, 2001, 14 : 241 - 260
[8] A NOTE ON THE LAW OF LARGE NUMBERS FOR DIRECTED RANDOM-WALKS IN RANDOM-ENVIRONMENTS
HORVATH, L
SHAO, QM
[J]. STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1994, 54 (02) : 275 - 279
[9] Dynamic Zd-random walks in a random scenery:: A strong law of large numbers
Guillotin-Plantard, N
[J]. JOURNAL OF THEORETICAL PROBABILITY, 2001, 14 (01) : 241 - 260
[10] Large deviations for random walks in a random environment
Varadhan, SRS
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2003, 56 (08) : 1222 - 1245

← 1 2 3 4 5 →