2011
DOI: 10.1007/s10440-011-9641-7
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Theorems on Large Deviations for Randomly Indexed Sum of Weighted Random Variables

Abstract: In this paper, we consider a random variable Z t = Nt i=1 a i X i , where X, X 1 , X 2 , . . . are independent identically distributed random variables with mean EX = μ and variance DX = σ 2 > 0. It is assumed that Z 0 = 0, 0 ≤ a i < ∞, and N t , t ≥ 0 is a non-negative integervalued random variable independent of X i , i = 1, 2, . . . . The paper is devoted to the analysis of accuracy of the standard normal approximation to the sumZ t = (DZ t ) −1/2 (Z t − EZ t ), large deviation theorems in the Cramer and po… Show more

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Cited by 1 publication
(9 citation statements)
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“…(6) in two cases: µ = 0 and µ = 0 by pointing out the difference between them. It should be noted that large deviations when µ = 0 have been already considered in our papers [1,2], thus in this instance we pointed only some results without proofs.…”
Section: Introductionmentioning
confidence: 80%
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“…(6) in two cases: µ = 0 and µ = 0 by pointing out the difference between them. It should be noted that large deviations when µ = 0 have been already considered in our papers [1,2], thus in this instance we pointed only some results without proofs.…”
Section: Introductionmentioning
confidence: 80%
“…For the examples when N obey Poisson, binomial, negative binomial distributions, and for discount instance of large deviations we refer to our papers [2,21].…”
Section: Large Deviation Theorems and Exponential Inequalitiesmentioning
confidence: 99%
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