IJPAM: Volume 40, No. 2 (2007)

IMPROVEMENT OF THE CONVERGENCE
RATE OF THE DISCOUNTED LIMIT THEOREM

Stasys Steišunas
Institute of Mathematics and Informatics
Akademijos 4, Vilnius, 08663, LITHUANIA
e-mail: stst@ktl.mii.lt


Abstract.Let $\xi _v=\sum\limits_{k = 0}^{\infty}v^k\xi _k$, where $0\leq v \leq 1$ and $\xi _0, \;\xi _1,\; \xi _2,\;\ldots $ be a sequence of independent and identically distributed random variables with the mean $E\xi _0=\mu <\infty$ and variance $\sigma ^2=E(\xi _0-\mu )^2<\infty$. The author considers the approximation of the distribution funtion of the normed sum of the random variable $Z_v=\sqrt{1-v} \sigma ^{-1} (\xi _v-\mu (1-v)^{-1})$ . Its estimate was obtained through pseudomoments.

Received: July 21, 2007

AMS Subject Classification: 60G30, 60G40, 60G50, 60G20

Key Words and Phrases: distributions, characteristic functions, discounted limit theorems, normal distribution function, Berry-Esseen Theorem

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 40
Issue: 2