Exact convergence rate of the local limit theorem for a branching random walk in a time-dependent random environment on d-dimensional integer lattice

2021 ◽  
pp. 1-24
Author(s):  
Zhiqiang Gao ◽  
Xiaoyan Zhang
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Convergence Rate ◽  
Random Environment ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Integer Lattice ◽  
Time Dependent ◽  
Branching Random Walk

A local limit theorem for random walk maxima with heavy tails

2002 ◽  
Vol 56 (4) ◽  
pp. 399-404 ◽  
Author(s):  
Søren Asmussen ◽  
Vladimir Kalashnikov ◽  
Dimitrios Konstantinides ◽  
Claudia Klüppelberg ◽  
Gurami Tsitsiashvili
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Heavy Tails ◽  
Local Limit Theorem ◽  
Local Limit

scholarly journals DYNAMIC QUANTUM BERNOULLI RANDOM WALKS

2008 ◽  
Vol 11 (02) ◽  
pp. 213-229
Author(s):  
NADINE GUILLOTIN-PLANTARD ◽  
RENÉ SCHOTT
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Walks ◽  
Limit Theorems ◽  
Law Of Large Numbers ◽  
Large Deviation Principle ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Large Numbers

Quantum Bernoulli random walks can be realized as random walks on the dual of SU(2). We use this realization in order to study a model of dynamic quantum Bernoulli random walk with time-dependent transitions. For the corresponding dynamic random walk on the dual of SU(2), we prove several limit theorems (local limit theorem, central limit theorem, law of large numbers, large deviation principle). In addition, we characterize a large class of transient dynamic random walks.

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