TY - JOUR
AU - Aurelija Kasparavičiūtė
AU - Leonas Saulis
PY - 2010/12/21
Y2 - 2022/05/21
TI - Theorems on large deviations for the sum of random number of summands
JF - Lietuvos matematikos rinkinys
JA - LMR
VL - 51
IS - proc. LMS
SE - Articles
DO - 10.15388/LMR.2014.12
UR - https://www.journals.vu.lt/LMR/article/view/17872
AB - 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, . . . .
ER -