Factorization of Markov Chains

N. B. Yengibarian ()
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N. B. Yengibarian: BAO NAS RA

Journal of Theoretical Probability, 2004, vol. 17, issue 2, 459-481

Abstract: Abstract Existence of following factorization is proved: $$I - A = \left( {I - B} \right)\left( {I - C} \right).{\text{ }}\left( F \right)$$ Here A is a stochastic or semi-stochastic (substohastic) d×d matrix (d≤∞); I is the unit matrix; B and C are nonnegative, upper and lower triangular matrices. B is a semistochastic matrix; the diagonal entries of C are ≤1. An exact information on properties of matrices B and C are obtained in particular cases. Some results on existence of invariant distribution x for Markov chains in the cases of absence or presence of sources g of walking particles are obtained using the factorization (F). These problems described by homogeneous or nonhomogeneous equation (I−A)x=g.

Keywords: Markov chains; stochastic matrix; invariant distribution (search for similar items in EconPapers)
Date: 2004
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DOI: 10.1023/B:JOTP.0000020703.46248.19

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