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Factorization of Markov Chains

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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.

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Authors and Affiliations

  1. BAO NAS RA, 378433, Armenia

    N. B. Yengibarian (Head of Centre of Mathematical Physics)

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  1. N. B. Yengibarian
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Yengibarian, N.B. Factorization of Markov Chains. Journal of Theoretical Probability 17, 459–481 (2004). https://doi.org/10.1023/B:JOTP.0000020703.46248.19

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  • DOI: https://doi.org/10.1023/B:JOTP.0000020703.46248.19

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