Perturbation bounds for the stationary probabilities of a finite Markov chain

Author:

Haviv Moshe,Van Der Heyden Ludo

Abstract

This paper discusses perturbation bounds for the stationary distribution of a finite indecomposable Markov chain. Existing bounds are reviewed. New bounds are presented which more completely exploit the stochastic features of the perturbation and which also are easily computable. Examples illustrate the tightness of the bounds and their application to bounding the error in the Simon–Ando aggregation technique for approximating the stationary distribution of a nearly completely decomposable Markov chain.

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

Reference13 articles.

1. Weak ergodicity in non-homogeneous Markov chains

2. The Condition of a Finite Markov Chain and Perturbation Bounds for the Limiting Probabilities

3. Courtois P. J. (1977b) The error of aggregation: comments on Zarling's analysis. MBLE Research Laboratory Report R345, Brussels.

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