KYBERNETIKA

Kybernetika 40(2):257-272, 2004.

Stability Estimates of Generalized Geometric Sums and Their Applications

Evgueni Gordienko

Abstract:

The upper bounds of the uniform distance $\rho\left(\sum^\nu_{k=1}X_k,\sum^\nu_{k=1}\tilde{X}_k\right)$ between two sums of a random number $\nu$ of independent random variables are given. The application of these bounds is illustrated by stability (continuity) estimating in models in queueing and risk theory.

Keywords: geometric sum; upper bound for the uniform distance; stability; risk process; ruin probability;

AMS: 91B30; 60G50;