ANALYTICAL APPROACH TO THE STUDY OF HETEROGENEOUS MARKOV CHAINS WITH PIECEWISE CONSTANT CHANGES IN TRANSITION PROBABILITIES
Annotation
An analytical approach to the study of countable non-homogeneous Markov chains based on the z-transformation is proposed. Using two variants of the initial data for the transition probabilities of a Markov chain as an example, it is shown that estimates of the steady-state mode can significantly distort the understanding of the system behavior. Analytical procedures for obtaining probability functions for real and complex-conjugate eigenvalues of the transition probability matrix are described for the case when its elements change abruptly. Estimates are given for the boundaries of the onset of a steady-state mode in the clock time. The main calculations are illustrated by an assessment of the characteristics of Markov chains taking into account the influence of transition dynamics under variance of the state probabilities and the piecewise constant change in transition probabilities over the operating interval in clock time.
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