On the limit behaviour of finite-support bivariate discrete probability distributions under iterated partial summations

Abstract

Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under which the power method (known from matrix theory) can be used. Examples of both a converging sequence of distributions, with its limit, and an oscillating sequence which does not converge are presented.