Precise large deviation estimates for a one-dimensional random walk in a random environment

1999 ◽  
Vol 113 (2) ◽  
pp. 191-219 ◽  
Author(s):  
Agoston Pisztora ◽  
Tobias Povel ◽  
Ofer Zeitouni
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
Large Deviation ◽  
One Dimensional ◽  
Precise Large Deviation

scholarly journals Gumbel and Fréchet convergence of the maxima of independent random walks

2020 ◽  
Vol 52 (1) ◽  
pp. 213-236 ◽  
Author(s):  
Thomas Mikosch ◽  
Jorge Yslas
Keyword(s):  
Random Walk ◽  
Random Walks ◽  
Point Process ◽  
Asymptotic Theory ◽  
Large Deviation ◽  
Moment Generating Function ◽  
Independent Random Variables ◽  
Finite Moment ◽  
Process Convergence ◽  
Precise Large Deviation

AbstractWe consider point process convergence for sequences of independent and identically distributed random walks. The objective is to derive asymptotic theory for the largest extremes of these random walks. We show convergence of the maximum random walk to the Gumbel or the Fréchet distributions. The proofs depend heavily on precise large deviation results for sums of independent random variables with a finite moment generating function or with a subexponential distribution.

scholarly journals Tail estimates for one-dimensional random walk in random environment

1996 ◽  
Vol 181 (3) ◽  
pp. 667-683 ◽  
Author(s):  
Amir Dembo ◽  
Yuval Peres ◽  
Ofer Zeitouni
Keyword(s):  
Random Walk ◽  
Random Environment ◽  
One Dimensional
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