scholarly journals Self-intersection local times of additive processes: Large deviation and law of the iterated logarithm

2006 ◽  
Vol 116 (9) ◽  
pp. 1236-1253 ◽  
Author(s):  
Xia Chen
Keyword(s):  
Large Deviation ◽  
Local Times ◽  
Additive Processes ◽  
Iterated Logarithm ◽  
Intersection Local Times

scholarly journals Chover-Type Laws of the Iterated Logarithm for Kesten-Spitzer Random Walks in Random Sceneries Belonging to the Domain of Stable Attraction

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Wensheng Wang ◽  
Anwei Zhu
Keyword(s):  
Random Walk ◽  
Large Deviation ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Domain Of Attraction ◽  
Stable Law ◽  
Iterated Logarithm ◽  
Cluster Set ◽  
Random Scenery ◽  
Unique Integer

Let X={Xi,i≥1} be a sequence of real valued random variables, S0=0 and Sk=∑i=1kXi  (k≥1). Let σ={σ(x),x∈Z} be a sequence of real valued random variables which are independent of X’s. Denote by Kn=∑k=0nσ(⌊Sk⌋)  (n≥0) Kesten-Spitzer random walk in random scenery, where ⌊a⌋ means the unique integer satisfying ⌊a⌋≤a<⌊a⌋+1. It is assumed that σ’s belong to the domain of attraction of a stable law with index 0<β<2. In this paper, by employing conditional argument, we investigate large deviation inequalities, some sufficient conditions for Chover-type laws of the iterated logarithm and the cluster set for random walk in random scenery Kn. The obtained results supplement to some corresponding results in the literature.

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