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
Citation
Bernhard, James. 2013. "The Geometry of Markov Chain Limit Theorems." Markov Processes And Related Fields 19(1): 99-124.