Strong Limit Theorems in Non-Commutative Probability

Author(s):  
Ryszard Jajte
Keyword(s):  
Author(s):  
Zhengyan Lin ◽  
Chuanrong Lu
Keyword(s):  

2021 ◽  
Vol 58 (2) ◽  
pp. 263-273
Author(s):  
Andrei N. Frolov

Fifty years ago P. Erdős and A. Rényi published their famous paper on the new law of large numbers. In this survey, we describe numerous results and achievements which are related with this paper or motivated by it during these years.


2008 ◽  
Vol 78 (14) ◽  
pp. 2018-2023 ◽  
Author(s):  
Weiguo Yang ◽  
Xue Yang
Keyword(s):  

1976 ◽  
Vol 13 (4) ◽  
pp. 696-706 ◽  
Author(s):  
David Burman

Particles enter a finite-state system and move according to independent sample paths from a semi-Markov process. Strong limit theorems are developed for the ratio of the flow of particles from states i to j and the flow out of When the cumulative arrival of particles into the system up to time t, A (t) ∼ λtα, then a.s. When A (t)∼ λekt, then the flow between states must be normalized by the Laplace–Stieltjes transform of the conditional holding time distribution, in order to make the ratio an unbiased estimator of ρij.


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