A remark on the central limit question for dependent random variables

1980 ◽  
Vol 17 (01) ◽  
pp. 94-101 ◽  
Author(s):  
Richard C. Bradley
Keyword(s):  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
Stable Limit ◽  
Limit Laws ◽  
Dependent Random Variables ◽  
Asymptotically Normal ◽  
Second Moments

Given a strictly stationary sequence {Xk, k= …, −1,0,1, …} of r.v.'s one defines forn= 1, 2, 3 …,. Here an example of {Xk} is given with finite second moments, for which Var(X1+ … +Xn)→∞ andρn→ 0 asn→∞, but (X1+ … +Xn) fails to be asymptotically normal; instead there is partial attraction to non-stable limit laws.

A remark on the central limit question for dependent random variables

1980 ◽  
Vol 17 (1) ◽  
pp. 94-101 ◽  
Author(s):  
Richard C. Bradley
Keyword(s):  
Central Limit ◽  
Random Variables ◽  
Stationary Sequence ◽  
Stable Limit ◽  
Limit Laws ◽  
Dependent Random Variables ◽  
Asymptotically Normal ◽  
Second Moments

Given a strictly stationary sequence {Xk, k = …, −1,0,1, …} of r.v.'s one defines for n = 1, 2, 3 …, . Here an example of {Xk} is given with finite second moments, for which Var(X1 + … + Xn)→∞ and ρ n → 0 as n→∞, but (X1 + … + Xn) fails to be asymptotically normal; instead there is partial attraction to non-stable limit laws.

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