Limit Theorems for Sums of Independent Random Variables with Values in Hilbert Space

1973 ◽  
Vol 17 (2) ◽  
pp. 199-217 ◽  
Author(s):  
V. M. Kruglov
Keyword(s):  
Hilbert Space ◽  
Limit Theorems ◽  
Random Variables ◽  
Independent Random Variables

scholarly journals Limit theorems for triangular arrays under a relaxed asymptotic negligibility condition

1987 ◽  
Vol 42 (1) ◽  
pp. 117-128 ◽  
Author(s):  
Miloslav Jirina
Keyword(s):  
Asymptotic Behavior ◽  
Classical Theory ◽  
Limit Theorems ◽  
Random Variables ◽  
Triangular Array ◽  
Independent Random Variables ◽  
Triangular Arrays

AbstractLet {Xnk} be a triangular array of independent random variables satisfying the so-called tail-negligibility condition, i.e. such that Prob{|Xnk| > a} → 0 as both k, n → ∞. It is also assumed that for each fixed k, Xnk converges in distribution as n → ∞. Theorems on the asymptotic behavior of the row sums of the array, analogous to those of the classical theory under the uniform negligibility condition, are presented.

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