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. An oscillating sequence of distributions, a phenomenon which has never been reported before, is presented.