scholarly journals A Log-scale Limit Theorem for One-dimensional Random Walks in Random Environments

2005 ◽  
Vol 10 (0) ◽  
pp. 244-253
Author(s):  
Alexander Roitershtein
Keyword(s):  
Limit Theorem ◽  
Random Walks ◽  
Random Environments ◽  
One Dimensional ◽  
Scale Limit

The almost sure central limit theorem for one-dimensional nearest-neighbour random walks in a space-time random environment

2004 ◽  
Vol 41 (01) ◽  
pp. 83-92 ◽  
Author(s):  
Jean Bérard
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Walks ◽  
Central Limit ◽  
Random Environment ◽  
Space Time ◽  
Nearest Neighbour ◽  
One Dimensional ◽  
The Central Limit Theorem ◽  
Almost All

The central limit theorem for random walks on ℤ in an i.i.d. space-time random environment was proved by Bernabeiet al.for almost all realization of the environment, under a small randomness assumption. In this paper, we prove that, in the nearest-neighbour case, when the averaged random walk is symmetric, the almost sure central limit theorem holds for anarbitrarylevel of randomness.

Limit theorems for one-dimensional diffusions and random walks in random environments

1989 ◽  
Vol 80 (4) ◽  
pp. 501-541 ◽  
Author(s):  
Kiyoshi Kawazu ◽  
Yozo Tamura ◽  
Hiroshi Tanaka
Keyword(s):  
Random Walks ◽  
Limit Theorems ◽  
Random Environments ◽  
One Dimensional
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