Numerical Approximation of Drazin Inverse in Markov Chain Theory
2014
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Thesis / Dissertation Description
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.
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