Title

The Geometry Of Markov Chain Limit Theorems

Document Type

Article

Publication Date

1-1-2013

Publication Title

Markov Processes And Related Fields

Department

Mathematics and Computer Science

Abstract

In this paper, we use a geometric viewpoint to prove several of the fundamental theorems on the convergence of Markov chains. In particular, we determine the long-term behavior of Markov chains geometrically both when they are irreducible and aperiodic and when they are not. By viewing the transition matrix of a Markov chain as a linear transformation from the standard simplex to itself, we simplify the traditional, matrix-based descriptions and proofs of the long-term behavior of Markov chains.

Volume

19

Issue

1

pp.

99-124

ISSN

1024-2953

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