Local limit theorems for the probability of large deviations for the maximum of sums of independent random variables

1978 ◽  
Vol 18 (1) ◽  
pp. 1-19
Author(s):  
A. Aleškevičienė
Keyword(s):  
Large Deviations ◽  
Limit Theorems ◽  
Random Variables ◽  
Local Limit ◽  
Independent Random Variables ◽  
Local Limit Theorems

scholarly journals The discounted local limit theorems for large deviations

2008 ◽  
Vol 48 ◽  
Author(s):  
Leonas Saulis ◽  
Dovilė Deltuvienė
Keyword(s):  
Large Deviations ◽  
Density Function ◽  
Limit Theorems ◽  
Distribution Density ◽  
Normal Approximation ◽  
Random Variables ◽  
Local Limit ◽  
Distribution Density Function ◽  
Local Limit Theorems

Theorems of large deviations, both in the Cramer zone and the Linnik power zones, for the normal approximation of the distribution density function of normalized sum Sv = \sum∞ k=0 vkXk, 0 < v < 1, of i.i.d. random variables (r.v.) X0, X1, . . . satisfying the generalized Bernstein’s condition are obtained.

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