Estimation of First Returning Speed in Null Recurrent Continuous-Time Markov Chains

TL;DR

This paper introduces a new approach to analyze null-recurrent continuous-time Markov chains by linking them to electric network theory, enabling systematic estimation of their first returning speed.

Contribution

It provides a novel method using electric network techniques to estimate the first returning speed in null recurrent CTMCs, especially birth-death processes.

Findings

Established a connection between null-recurrent CTMCs and electric networks.

Developed a general method for estimating first returning speed.

Provided illustrative examples demonstrating the method.

Abstract

This paper establishes a novel connection between null-recurrent CTMCs and electric networks, offering a systematic classification of null-recurrent behavior based on the first returning speed. By leveraging techniques from electric network theory, we present a general method for estimating the first returning speed of null recurrent birth-death processes and provide some important examples.