danДоклады Национальной академии наук БеларусиDoklady of the National Academy of Sciences of Belarus1561-83232524-2431The Republican Unitary Enterprise Publishing House "Belaruskaya Navuka"10.29235/1561-8323-2026-70-3-191-200dan-1309Research ArticleМАТЕМАТИКАMATHEMATICSНеоднородные цепи Маркова высокого порядка: модели и их вероятностно-статистический анализNon-homogeneous high-order Markov chains: models and their probabilistic-statistical analysisХаринЮ. С.KharinYu. S.

Харин Юрий Семенович – академик, д-р физ.-мат. наук, профессор, директор

пр. Независимости, 4, 220030, Минск

Kharin Yuriy S. – Academician, D. Sc. (Physics and Mathematics), Professor, Director

4, Nezavisimosti Ave., 220030, Minsk

kharin@bsu.byНаучно-исследовательский институт прикладных проблем математики и информатики Белорусского государственного университетаБеларусьResearch Institute for Applied Problems of Mathematics and Informatics of the Belarusian State UniversityBelarus202609072026703191200Copyright © Харин Ю.С., 20262026Харин Ю.С.Kharin Y.S.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://doklady.belnauka.by/jour/article/view/1309

Сообщение посвящено развитию теории вероятностно-статистического анализа неоднородных цепей Маркова высокого порядка, для которых матрица вероятностей одношаговых переходов допускает изменение во времени. Построены модели детерминировано-неоднородных и стохастически-неоднородных цепей Маркова высокого порядка, исследованы их вероятностные свойства и предложены подходы к статистическому оцениванию параметров этих моделей.

The paper is devoted to the development of probabilistic and statistical analysis of non-homogeneous high-order Markov chains for cases in which the matrix of one-step transition probabilities is time-varying. Models for deterministically non-homogeneous and stochastically non-homogeneous high-order Markov chains are constructed. Probabilistic properties of these models are analyzed and some approaches to statistical estimation of the model parameters are proposed.

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The authors declare that there are no conflicts of interest present.