scholarly journals Large deviations and wandering exponent for random walk in a dynamic beta environment

2019 ◽  
Vol 47 (4) ◽  
pp. 2186-2229 ◽  
Author(s):  
Márton Balázs ◽  
Firas Rassoul-Agha ◽  
Timo Seppäläinen
Keyword(s):  
Random Walk ◽  
Large Deviations

scholarly journals Large Deviations for a Random Walk Model with State-Dependent Noise

2003 ◽  
Vol 42 (3) ◽  
pp. 810-838
Author(s):  
Michelle Boué ◽  
Daniel Hernández-Hernández ◽  
Richard S. Ellis
Keyword(s):  
Random Walk ◽  
Large Deviations ◽  
Random Walk Model ◽  
State Dependent

The geometric convergence rate of a Lindley random walk

1997 ◽  
Vol 34 (3) ◽  
pp. 806-811
Author(s):  
Robert B. Lund
Keyword(s):  
Random Walk ◽  
Convergence Rate ◽  
Large Deviations ◽  
Total Variation ◽  
Short Proof ◽  
Random Variables ◽  
Invariant Distribution ◽  
Initial State ◽  
Geometric Convergence ◽  
Independent And Identically Distributed

Let {Xn} be the Lindley random walk on [0,∞) defined by . Here, {An} is a sequence of independent and identically distributed random variables. When for some r > 1, {Xn} converges at a geometric rate in total variation to an invariant distribution π; i.e. there exists s > 1 such that for every initial state . In this communication we supply a short proof and some extensions of a large deviations result initially due to Veraverbeke and Teugels (1975, 1976): the largest s satisfying the above relationship is and satisfies φ ‘(r0) = 0.

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