Computer investigation of the Rate of Convergence of Lepage Type Series to α-Stable Random Variables

The aim of the paper is to present the results of computer experiments that allowed us to investigate some of the properties of LePage series representations of α-stable random variables and to check their usefulness to computer simulation of Lévy motion. We base our study on the explicitly obtained formula for the expectation , where , with τ j 's denoting the arrival times of a Poisson process and appropriately chosen discrete random variables, and where X denotes an a.s. limit of the sequence {X n }. We conclude that as far as computer simulations are concerned the sums X n are not the most suitable means of approximation of X.