Title

Numerical Approximation of Drazin Inverse in Markov Chain Theory

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

Date of Award

Fall 2014

Abstract

One generalized inverse of the matrix Q is the Drazin inverse, Q^#. Many importantquantities in Markov chain theory can be expressed in terms of Q^#, where Q = I - P, thematrix P being the transition probability matrix of the chain. Previous work has establishedconditions and algorithms for estimating Q^# in a general setting but specific results are lacking.In this study, estimation of Q^# is considered for finite state Markov chains. Optimal parametersettings and convergence rates of the algorithms are examined.

Advisor

Thomas Boucher

Subject Categories

Mathematics | Physical Sciences and Mathematics

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