Kybernetika 40 no. 2, 257-272, 2004

Stability estimates of generalized geometric sums and their applications

Evgueni Gordienko


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.