Geodesic
Calculation of the number of states in binary Markov stochastic models
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 191-200.

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This paper derives exact and approximate formulas for the distribution, average values and variances of the number of units on the segments of binary Markov sequences. Various ways to calculate these formulas are proposed. Estimates of the errors are given. An example of the calculation for a binary Markov model of the precipitation process is presented. 
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L. Ya. Saveliev. Calculation of the number of states in binary Markov stochastic models. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 18 (2015) no. 2, pp. 191-200. http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a6/

[1] Drobyshev A. D., Marchenko A. S., Ogorodnikov V. A., Chizhikov V. D., “Statisticheskaya struktura vremennykh ryadov sutochnykh summ zhidkikh osadkov v ravninnoj chasti Novosibirskoj oblasti”, Tr. ZapSib NII Goskomgidrometa, 86, 1989, 44–74

[2] Kemeni Dzh., Snell Dzh., Konechnye tsepi Markova, Nauka, M., 1970

[3] Markov A. A., Ischislenie veroyatnostej, Tipografiya imperatorskoj akademii nauk, SPb., 1913

[4] Savel'ev L. Ya., “Sluchajnye sootvetstviya, dvoichnye matritsy i serii”, Diskretnaya matematika, 11:4 (1999), 3–26 | DOI | MR | Zbl

[5] Savel'ev L., Balakin S., Konechnye markovskie tsepi i serii (teoriya i prilozheniya), LAP LAMBERT Academic Publishing, 2012

[6] Uitteker E. T., Vatson Dzh. N., Kurs sovremennogo analiza, V 2-kh tomakh, Gos. izd-vo fiz.-mat. literatury, M., 1963