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.

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.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

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