Open AccessTheorems on large deviations for the sum of random number of summands
Author(s) -
Aurelija Kasparavičiūtė,
L. Saulis
Publication year - 2010
Publication title -
lietuvos matematikos rinkinys
Language(s) - English
Resource type - Journals
eISSN - 2335-898X
pISSN - 0132-2818
DOI - 10.15388/lmr.2014.12
Subject(s) - independent and identically distributed random variables , mathematics , random variable , variance (accounting) , large deviations theory , convergence (economics) , combinatorics , variable (mathematics) , discrete mathematics , statistics , mathematical analysis , accounting , economics , business , economic growth
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, . . . .