On the global central limit theorem for π-mixing random variables

1995 ◽  
Vol 35 (2) ◽  
pp. 185-196
Author(s):  
J. Sunklodas
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Mixing Random Variables

scholarly journals Convergence of Weighted Linear Process forρ-Mixing Random Variables

2007 ◽  
Vol 2007 ◽  
pp. 1-7
Author(s):  
Guang-Hui Cai
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Linear Process ◽  
Functional Central Limit Theorem ◽  
Mixing Sequences ◽  
Functional Central Limit ◽  
Mixing Random Variables

A central limit theorem and a functional central limit theorem are obtained for weighted linear process ofρ-mixing sequences for theXt=∑i=0∞aiYt−i, where{Yi,0≤i<∞}is a sequence ofρ-mixing random variables withEYi=0,0<EYi2<∞,∑i=1∞ρ(2i)<∞. The results obtained generalize the results of Liang et al. (2004) toρ-mixing sequences.

scholarly journals Central limit theorem for linear processes generated by IID random variables under the sub-linear expectation

2021 ◽  
Vol 36 (2) ◽  
pp. 243-255
Author(s):  
Wei Liu ◽  
Yong Zhang
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Invariance Principle ◽  
Random Variables ◽  
Probability Measures ◽  
Linear Processes ◽  
The Central Limit Theorem

AbstractIn this paper, we investigate the central limit theorem and the invariance principle for linear processes generated by a new notion of independently and identically distributed (IID) random variables for sub-linear expectations initiated by Peng [19]. It turns out that these theorems are natural and fairly neat extensions of the classical Kolmogorov’s central limit theorem and invariance principle to the case where probability measures are no longer additive.

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