Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/30347
Title: Convergence of a second order Markov chain
Authors: Hu, S
Qi, L 
Keywords: Nonnegative tensor
Second order Markov chain
Transition probability tensor
Issue Date: 2014
Publisher: Elsevier
Source: Applied mathematics and computation, 2014, v. 241, p. 183-192 How to cite?
Journal: Applied mathematics and computation 
Abstract: In this paper, we consider convergence properties of a second order Markov chain. Similar to a column stochastic matrix being associated to a Markov chain, a transition probability tensor P of order 3 and dimension n is associated to a second order Markov chain with n states. For this P, define FP as FP(x) = Px2 on the n-1 dimensional standard simplex £Gn. If 1 is not an eigenvalue of FP on £Gn and P is irreducible, then there exists a unique fixed point of FP on £Gn. In particular, if every entry of P is greater than 12n, then 1 is not an eigenvalue of FP on £Gn. Under the latter condition, we further show that the second order power method for finding the unique fixed point of FP on £Gn is globally linearly convergent and the corresponding second order Markov process is globally R-linearly convergent.
URI: http://hdl.handle.net/10397/30347
ISSN: 0096-3003
EISSN: 1873-5649
DOI: 10.1016/j.amc.2014.05.011
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