scholarly journals A local limit theorem and loss of rotational symmetry of planar symmetric simple random walk

2018 ◽  
Vol 371 (4) ◽  
pp. 2553-2573
Author(s):  
Christian Beneš
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Rotational Symmetry ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Simple 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.

A large deviation local limit theorem

1989 ◽  
Vol 105 (3) ◽  
pp. 575-577 ◽  
Author(s):  
R. A. Doney
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Random Walks ◽  
Large Deviation ◽  
Local Limit Theorem ◽  
Local Limit ◽  
Large Deviation Result

The following elegant one-sided large deviation result is given by S. V. Nagaev in [2].Theorem 0. Suppose that {Sn,n ≤ 0} is a random walk whose increments Xi are independent copies of X, where(X) = 0 andPr{X > x} ̃ x−αL(x) as x→ + ∞,and where 1 < α < ∞ and L is slowly varying at ∞. Then for any ε > 0 and uniformly in x ≥ εnPr{Sn > x} ̃ n Pr{X > x} as n→∞.It is the purpose of this note to point out that for lattice-valued random walks there is an analogous local limit theorem.

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