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Analytical Approach to the Selective Search of State Probability Functions for Markov Processes
https://doi.org/10.17586/0021-3454-2025-68-6-465-481
Abstract
An analytical approach to the study of Markov processes is proposed. Using an algorithm for selective search of input–output operators and simple analytical procedures, time probability functions are obtained for real and complex conjugate eigenvalues of the transition intensity matrix. Estimates of the time of onset of the stationary regime are given. Examples of the analysis of homogeneous and heterogeneous Markov processes with piecewise constant transition intensities, non-Markov processes with pseudo-states generated by Erlang flows, as well as substantiation of requirements for the intensity of restoration (efficiency of the repair body) in a technical system are considered. The main results are illustrated by probability estimation in a rigorous analytical form.
About the Author
A. V. Zemskov
Admiral Makarov State University of Maritime and Inland Shipping
Russian Federation
Russian Federation
Alexey V. Zemskov —Dr. Sci., Professor; Department of Mathematical Modeling and Applied Informatics; Professor;
St. Petersburg.
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Review
For citations:
Zemskov A.V. Analytical Approach to the Selective Search of State Probability Functions for Markov Processes. Journal of Instrument Engineering. 2025;68(6):465-481. (In Russ.) https://doi.org/10.17586/0021-3454-2025-68-6-465-481
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