scholarly journals A strong limit theorem for the oscillation modulus of the uniform empirical quantile process

1984 ◽  
Vol 17 (1) ◽  
pp. 127-136 ◽  
Author(s):  
David M. Mason
Keyword(s):  
Limit Theorem ◽  
Strong Limit ◽  
Quantile Process ◽  
Strong Limit Theorem ◽  
Oscillation Modulus

A representation for the limiting random variable of a branching process with infinite mean and some related problems

1978 ◽  
Vol 15 (02) ◽  
pp. 225-234 ◽  
Author(s):  
Harry Cohn ◽  
Anthony G. Pakes
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Convergence Rate ◽  
Branching Process ◽  
Extreme Value Distribution ◽  
Random Variable ◽  
Random Sum ◽  
Strong Limit ◽  
Strong Limit Theorem ◽  
Watson Process

It is known that for a Bienaymé– Galton–Watson process {Zn } whose mean m satisfies 1 < m < ∞, the limiting random variable in the strong limit theorem can be represented as a random sum of i.i.d. random variables and hence that convergence rate results follow from a random sum central limit theorem. This paper develops an analogous theory for the case m = ∞ which replaces ‘sum' by ‘maximum'. In particular we obtain convergence rate results involving a limiting extreme value distribution. An associated estimation problem is considered.

THE STRONG LIMIT THEOREM FOR RELATIVE ENTROPY DENSITY RATES BETWEEN TWO ASYMPTOTICALLY CIRCULAR MARKOV CHAINS

2018 ◽  
Vol 33 (2) ◽  
pp. 161-171
Author(s):  
Ying Tang ◽  
Weiguo Yang ◽  
Yue Zhang
Keyword(s):  
Limit Theorem ◽  
Markov Chains ◽  
Relative Entropy ◽  
Entropy Density ◽  
Strong Limit ◽  
Strong Limit Theorem

In this paper, we are going to study the strong limit theorem for the relative entropy density rates between two finite asymptotically circular Markov chains. Firstly, we prove some lammas on which the main result based. Then, we establish two strong limit theorem for non-homogeneous Markov chains. Finally, we obtain the main result of this paper. As corollaries, we get the strong limit theorem for the relative entropy density rates between two finite non-homogeneous Markov chains. We also prove that the relative entropy density rates between two finite non-homogeneous Markov chains are uniformly integrable under some conditions.

scholarly journals A strong limit theorem on gambling systems

2003 ◽  
Vol 84 (2) ◽  
pp. 262-273 ◽  
Author(s):  
Wen Liu ◽  
Jinting Wang
Keyword(s):  
Limit Theorem ◽  
Strong Limit ◽  
Strong Limit Theorem
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