An extension of central limit theorem for randomly indexed m-dependent random variables

Filomat ◽  
2017 ◽  
Vol 31 (14) ◽  
pp. 4369-4377 ◽  
Author(s):  
Stefano Belloni
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Number ◽  
Random Variables ◽  
Random Variable ◽  
Positive Random Variable ◽  
Dependent Random Variables

In this note, we prove a conjecture of Shang about the sum of a random number Nn of m-dependent random variables. The random number Nn is supposed to converge in probability toward a positive random variable.

scholarly journals A central limit theorem for randomly indexed m-dependent random variables

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 713-717 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Number ◽  
Moving Average ◽  
Random Variables ◽  
Dependent Random Variables ◽  
Average Sequence

In this note, we prove a central limit theorem for the sum of a random number Nn of m-dependent random variables. The sequence Nn and the terms in the sum are not assumed to be independent. Moreover, the conditions of the theorem are not stringent in the sense that a simple moving average sequence serves as an example.

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