A Subgeometric Convergence Formula for Total-variation Error of the Level-increment Truncation Approximation of M/G/1-type Markov Chains

TL;DR

This paper derives a subgeometric convergence formula for the total-variation error in the level-increment truncation approximation of M/G/1-type Markov chains, aiding in understanding the approximation's accuracy.

Contribution

It provides the first subgeometric convergence formula for the total-variation error in LI truncation of M/G/1-type Markov chains, enhancing theoretical understanding.

Findings

Subgeometric convergence formula established

Quantifies error between stationary distribution and approximation

Improves accuracy analysis of LI truncation method

Abstract

This paper considers the level-increment (LI) truncation approximation of M/G/1-type Markov chains. The LI truncation approximation is usually used to implement Ramaswami's recursion for the stationary distribution in M/G/1-type Markov chains. The main result of this paper is a subgeometric convergence formula for the total-variation distance between the stationary distribution and its LI truncation approximation.