Non trivial limit distributions for transient renewal chains

TL;DR

This paper investigates the long-term behavior of renewal sequences linked to specific transient renewal Markov chains, focusing on the existence of limit laws in this context.

Contribution

It introduces new results on the asymptotic behavior and limit distributions for renewal sequences in transient Markov chain settings.

Findings

Established conditions for the existence of limit laws

Derived explicit asymptotic formulas

Identified classes of chains with non-trivial limit distributions

Abstract

In this work we study the asymptotic of renewal sequences associated with certain transient renewal Markov chains and enquire about the existence of limit laws in this set up.