IJPAM: Volume 13, No. 3 (2004)

COMPARISON BETWEEN DISTRIBUTIONS OF
SUMS OF RANDOM VARIABLES AND ROBUSTNESS
OF SOME APPLIED STOCHASTIC MODELS

E. Gordienko$^1$, J. Ruiz de Chávez$^2$
$^{1,2}$Department of Mathematics
UAM-Iztapalapa
Av. San Rafael Atlixco No. 186, Col. Vicentina
A.P. 55-534, C.P. 09340 Iztapalapa
Mexico, D.F., MEXICO
$^1$e-mail: gord@xanum.uam.mx
$^2$e-mail: jrch@xanum.uam.mx


Abstract.The aim of the paper is to show that the probability metric approach to the comparison between distributions of two sums of random variables can be successfully applied in the analysis of stability (robustness) of many stochastic models with optimization applications. For this purpose we extend some known estimates of the rate of convergence in the central limit theorem to compare sums of random variables not necessarily Gaussian. Then we use the inequalities obtained to get new quantitative stability estimates in the following models: the S. Andersen risk process, renewal functions, optimization of the replacement period in the block-replacement model, optimization of the initial capital securing a prescribed risk in the classical risk model and a certain ingredient of a dam model with compound Poisson inputs.

Received: February 20, 2004

AMS Subject Classification: 60E15, 60K10

Key Words and Phrases: uniform metric and pseudomoments, sums of random variables, upper bounds of proximity, risk process, renewal function, replacement policy

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 3