The discount version of large deviations for a randomly indexed sum of random variables

Abstract

In this paper, we consider a compound random variable Z = \sum^N_{j=1} vjXj , where 0 0 are independent of a non-negative integer-valued random variable N. It should be noted that, in this scheme of summation, we must consider two cases: μ\neq 0 and μ = 0. The paper is designated to the research of the upper estimates of normal approximation to the sum ˜ Z = (Z −EZ)(DZ)−1/2, theorems on large deviations in the Cramer and power Linnik zones and exponential inequalities for P( ˜ Z > x).

Keywords

• cumulant
• large deviations theorems
• discounted limit theorems
• normal approximation
• random number of summands