Theorems on large deviations for the sum of random number of summands
Articles
Aurelija Kasparavičiūtė
Vilniaus Gedimino technikos universitetas
Leonas Saulis
Vilniaus Gedimino technikos universitetas
Published 2010-12-21
https://doi.org/10.15388/LMR.2014.12
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Keywords

cumulant
large deviations
compound Poisson process

How to Cite

Kasparavičiūtė A. and Saulis L. (2010) “Theorems on large deviations for the sum of random number of summands”, Lietuvos matematikos rinkinys, 51(proc. LMS), pp. 459–464. doi: 10.15388/LMR.2014.12.

Abstract

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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