A Limit Theorem for a Random Walk in a Random Environment

1989 ◽  
Vol 33 (2) ◽  
pp. 228-238 ◽  
Author(s):  
A. V. Letchikov
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Environment

On the non-recurrent random walk in a random environment

2018 ◽  
Vol 28 (3) ◽  
pp. 139-156 ◽  
Author(s):  
Valeriy I. Afanasyev
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Environment ◽  
Recurrent Random Walk ◽  
High Level ◽  
Transient Random Walk

Abstract For weakly transient random walk in a random environment that tend at −∞ the limit theorem for the time of hitting a high level is proved.

scholarly journals Path to survival for the critical branching processes in a random environment

2017 ◽  
Vol 54 (2) ◽  
pp. 588-602 ◽  
Author(s):  
Vladimir Vatutin ◽  
Elena Dyakonova
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Environment ◽  
Branching Process ◽  
Branching Processes ◽  
Functional Limit Theorem ◽  
Levy Process ◽  
Initial Part ◽  
Functional Limit ◽  
Critical Branching Process

Abstract A critical branching process {Zk, k = 0, 1, 2, ...} in a random environment is considered. A conditional functional limit theorem for the properly scaled process {log Zpu, 0 ≤ u < ∞} is established under the assumptions that Zn > 0 and p ≪ n. It is shown that the limiting process is a Lévy process conditioned to stay nonnegative. The proof of this result is based on a limit theorem describing the distribution of the initial part of the trajectories of a driftless random walk conditioned to stay nonnegative.

scholarly journals RANDOM WALK IN QUASI-PERIODIC RANDOM ENVIRONMENT

2009 ◽  
Vol 09 (01) ◽  
pp. 47-70 ◽  
Author(s):  
JULIEN BRÉMONT
Keyword(s):  
Random Walk ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Environment ◽  
Random Medium ◽  
Diophantine Condition ◽  
Finite Range ◽  
One Dimensional

We consider a one-dimensional random walk with finite range in a random medium described by an ergodic translation on a torus. For regular data and under a Diophantine condition on the translation, we prove a central limit theorem with deterministic centering.

Sign in / Sign up

Export Citation Format

Share Document