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

Katsuhisa Ouchi, Hiroyuki Masuyama

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.

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

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.
Paper Structure (2 sections, 2 equations)

This paper contains 2 sections, 2 equations.

Table of Contents

  1. Introduction
  2. Preliminaries