On the rate of convergence and large deviations in the invariance principle

1979 ◽  
Vol 11 (2) ◽  
pp. 260-260
Author(s):  
A. A. Borovkov
Keyword(s):  
Large Deviations ◽  
Rate Of Convergence ◽  
Invariance Principle

Large Deviations and Statistical Invariance Principle

1993 ◽  
Vol 37 (1) ◽  
pp. 7-13 ◽  
Author(s):  
A. A. Borovkov ◽  
A. A. Mogulskii
Keyword(s):  
Large Deviations ◽  
Invariance Principle

scholarly journals Theorems on large deviations for the sum of random number of summands

2010 ◽  
Vol 51 ◽  
Author(s):  
Aurelija Kasparavičiūtė ◽  
Leonas Saulis
Keyword(s):  
Large Deviations ◽  
Rate Of Convergence ◽  
Random Number ◽  
Normal Approximation ◽  
Random Variables ◽  
Random Variable ◽  
Compound Process ◽  
Independent Identically Distributed

In this paper, we present the rate of convergence of normal approximation and the theorem on large deviations for a compound process Zt = \sumNt i=1 t aiXi, where Z0 = 0 and ai > 0, of weighted independent identically distributed random variables Xi, i = 1, 2, . . . with  mean EXi = µ and variance DXi = σ2 > 0. It is assumed that Nt is a non-negative integervalued random variable, which depends on t > 0 and is independent of Xi, i = 1, 2, . . . .

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