On the Strong Ratio Limit Property for Discrete-Time Birth-Death Processes

TL;DR

This paper establishes a new sufficient condition based on transition probabilities for discrete-time birth-death processes to have the strong ratio limit property, unifying and extending previous criteria.

Contribution

It provides a comprehensive condition directly in terms of transition probabilities, covering all previously known sufficient conditions for the strong ratio limit property.

Findings

Derived a new sufficient condition for the strong ratio limit property.

Unified previous separate conditions into a single comprehensive criterion.

Applicable to all discrete-time birth-death processes with transition probabilities.

Abstract

A sufficient condition is obtained for a discrete-time birth-death process to possess the strong ratio limit property, directly in terms of the one-step transition probabilities of the process. The condition encompasses all previously known sufficient conditions.