scholarly journals Almost sure limit theorems for the maxima of some strongly dependent Gaussian sequences

2011 ◽  
Vol 62 (2) ◽  
pp. 635-640 ◽  
Author(s):  
Fuming Lin ◽  
Yu Fu ◽  
Yingying Jiang
Keyword(s):  
Limit Theorems ◽  
Almost Sure Limit Theorems

scholarly journals Almost Sure Limit Theorems for Multivariate General Standard Normal Sequences and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zhicheng Chen ◽  
Xinsheng Liu
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Almost Sure Convergence ◽  
Central Limit Theorems ◽  
Random Vectors ◽  
Standard Normal ◽  
Almost Sure Limit Theorems ◽  
General Standard

Under suitable conditions, the almost sure central limit theorems for the maximum of general standard normal sequences of random vectors are proved. The simulation of the almost sure convergence for the maximum is firstly performed, which helps to visually understand the theorems by applying to two new examples.

Almost sure limit theorems for the St. Petersburg game

1999 ◽  
Vol 45 (1) ◽  
pp. 23-30 ◽  
Author(s):  
István Berkes ◽  
Endre Csáki ◽  
Sándor Csörgő
Keyword(s):  
Limit Theorems ◽  
Almost Sure Limit Theorems

Almost sure limit theorems of extremes of complete and incomplete samples of stationary sequences

Extremes ◽  
2009 ◽  
Vol 13 (4) ◽  
pp. 463-480 ◽  
Author(s):  
Zuoxiang Peng ◽  
Zhichao Weng ◽  
Saralees Nadarajah
Keyword(s):  
Limit Theorems ◽  
Stationary Sequences ◽  
Almost Sure Limit Theorems

scholarly journals Variations around Eagleson’s theorem on mixing limit theorems for dynamical systems

2019 ◽  
Vol 40 (12) ◽  
pp. 3368-3374 ◽  
Author(s):  
SÉBASTIEN GOUËZEL
Keyword(s):  
Dynamical Systems ◽  
Probability Measure ◽  
Limit Theorems ◽  
Absolutely Continuous ◽  
Almost Sure Limit Theorems

Eagleson’s theorem asserts that, given a probability-preserving map, if renormalized Birkhoff sums of a function converge in distribution, then they also converge with respect to any probability measure which is absolutely continuous with respect to the invariant one. We prove a version of this result for almost sure limit theorems, extending results of Korepanov. We also prove a version of this result, in mixing systems, when one imposes a conditioning both at time 0 and at time $n$.

Almost sure limit theorems for random allocations

2005 ◽  
Vol 42 (2) ◽  
pp. 173-194
Author(s):  
István Fazekas ◽  
Alexey Chuprunov
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Domain ◽  
Almost Sure Limit Theorem ◽  
The Central Limit Theorem ◽  
Almost Sure Limit Theorems ◽  
Poisson Limit

Almost sure limit theorems are presented for random allocations. A general almost sure limit theorem is proved for arrays of random variables. It is applied to obtain almost sure versions of the central limit theorem for the number of empty boxes when the parameters are in the central domain. Almost sure versions of the Poisson limit theorem in the left domain are also proved.

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