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

TL;DR

This paper investigates the limit behavior of finite-support bivariate discrete probability distributions under iterated partial summations, revealing a novel oscillating sequence phenomenon using matrix theory.

Contribution

It introduces a method to determine the existence of limit distributions for finite-support bivariate distributions and reports the first observation of oscillating sequences.

Findings

Identified conditions for the existence of limit distributions.

Discovered an oscillating sequence phenomenon in the iterative process.

Applied matrix theory to analyze distribution convergence.

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.