Equivalence of Limit Theorems for Sums of Random Variables and Renewal Processes

2018 ◽  
pp. 1-25
Author(s):  
Valeriĭ V. Buldygin ◽  
Karl-Heinz Indlekofer ◽  
Oleg I. Klesov ◽  
Josef G. Steinebach
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Renewal Processes ◽  
Sums Of Random Variables

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).

scholarly journals The limit theorems for the sums of random variables related to a Markov chains. II

1969 ◽  
Vol 9 (3) ◽  
pp. 635-672
Author(s):  
V. Statulevičius
Keyword(s):  
Markov Chains ◽  
Limit Theorems ◽  
Random Variables ◽  
Sums Of Random Variables

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: В. А. Статулявичус. Предельные теоремы для сумм случайных величин связанных в цепь Маркова. II V. Statulevičius. Ribinės teoremos atsitiktinių dydžių, surištų į Markovo grandinę sumoms. II

Limit theorems in fluctuation theory

1973 ◽  
Vol 5 (03) ◽  
pp. 554-569 ◽  
Author(s):  
N. H. Bingham
Keyword(s):  
Random Walks ◽  
Discrete Time ◽  
Continuous Time ◽  
Limit Theorems ◽  
Recurrent Events ◽  
Random Variables ◽  
Fluctuation Theory ◽  
Partial Sums ◽  
Sums Of Random Variables ◽  
Independent Increments

We shall be concerned here with limit theorems arising in the fluctuation theory of random walks, processes with stationary independent increments, recurrent events and regenerative phenomena. In Section 1 on discrete time, we consider limit theorems for ladder-points (Theorem 1) and for maxima of partial sums of random variables (Theorem 2), and discuss some related questions. In Section 2 (Theorems 3 to 6) we consider the analogues of these results in continuous time.

Renewal theory in a random environment

1994 ◽  
Vol 116 (1) ◽  
pp. 179-190
Author(s):  
Laurence A. Baxter ◽  
Linxiong Li
Keyword(s):  
Stochastic Process ◽  
Random Environment ◽  
Limit Theorems ◽  
Random Variables ◽  
Renewal Theory ◽  
Renewal Processes ◽  
Conditional Distributions ◽  
The Future ◽  
Standard Limit

AbstractA random environment is modelled by an arbitrary stochastic process, the future of which is described by a σ-algebra. Renewal processes and alternating renewal processes are defined in this environment by considering the conditional distributions of random variables generated by the processes with respect to the σ-algebra. Generalizations of several of the standard limit theorems of renewal theory are derived.

Limit Theorems for Sums of Random Variables.

1987 ◽  
Vol 82 (398) ◽  
pp. 694
Author(s):  
Robert Lee Taylor ◽  
A. A. Borokov
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Sums Of Random Variables
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