C&SA | Contents

Volume 62 >>> № 1 JANUARY — FEBRUARY 2026

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UDC 519.2

Ya.I. Yeleyko
Ivan Franko National University of Lviv, Lviv, Ukraine,
yaroslav.yeleyko@lnu.edu.ua

A.Y. Drebot
Ivan Franko National University of Lviv, Lviv, Ukraine,
Andrii.Drebot.AMTS@lnu.edu.ua

MIXTURE OF ERGODIC MARKOV CHAINS

Abstract. This paper considers time series that represent a sequence of certain states, which can be modeled as a Markov chain. It is assumed that the chain describing the time series can be represented as a mixture of arbitrary ergodic independent Markov chains. A methodology for finding the coefficients of this mixture will be proposed, which is based on the application of the Ergodic Theorem.

Keywords: Markov chains, ergodic theorem, mixture of Markov chains, limiting distribution.

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