Non-Classical Limit Theorems

1971 ◽  
Vol 16 (1) ◽  
pp. 175-182 ◽  
Author(s):  
Yu. Yu. Machis
Keyword(s):  
Classical Limit ◽  
Limit Theorems

scholarly journals A Note on Rényi's ‘Record’ Problem and Engel's Series

2018 ◽  
Vol 61 (2) ◽  
pp. 363-369 ◽  
Author(s):  
Lulu Fang ◽  
Min Wu
Keyword(s):  
Number Theory ◽  
Large Deviations ◽  
Markov Processes ◽  
Classical Limit ◽  
Limit Theorems ◽  
London Math ◽  
Law Of Large Numbers ◽  
Record Times ◽  
Iterated Logarithm ◽  
Large Numbers

AbstractIn 1973, Williams [D. Williams, On Rényi's ‘record’ problem and Engel's series, Bull. London Math. Soc.5 (1973), 235–237] introduced two interesting discrete Markov processes, namely C-processes and A-processes, which are related to record times in statistics and Engel's series in number theory respectively. Moreover, he showed that these two processes share the same classical limit theorems, such as the law of large numbers, central limit theorem and law of the iterated logarithm. In this paper, we consider the large deviations for these two Markov processes, which indicate that there is a difference between C-processes and A-processes in the context of large deviations.

Applications of the key renewal theorem: crudely regenerative processes

1992 ◽  
Vol 29 (02) ◽  
pp. 384-395
Author(s):  
Richard F. Serfozo
Keyword(s):  
Classical Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Limit Function ◽  
Regenerative Processes ◽  
Renewal Theorem ◽  
Key Renewal Theorem ◽  
Derivatives Of

Limit Statements obtainable by the key renewal theorem are of the form EXt = v(t) + o(1), as t →∞. We show how to delineate the limit function v for processes X associated with crudely regenerative phenomena. Included are refinements of classical limit theorems for Markov and regenerative processes, limits of sums of stationary random variables, and limits for integrals and derivatives of EXt.

Applications of the key renewal theorem: crudely regenerative processes

1992 ◽  
Vol 29 (2) ◽  
pp. 384-395 ◽  
Author(s):  
Richard F. Serfozo
Keyword(s):  
Classical Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Limit Function ◽  
Regenerative Processes ◽  
Renewal Theorem ◽  
Key Renewal Theorem ◽  
Derivatives Of

Limit Statements obtainable by the key renewal theorem are of the form EXt = v(t) + o(1), as t →∞. We show how to delineate the limit function v for processes X associated with crudely regenerative phenomena. Included are refinements of classical limit theorems for Markov and regenerative processes, limits of sums of stationary random variables, and limits for integrals and derivatives of EXt.

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