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. 
@article{SJVM_2015_18_2_a6,
     author = {L. Ya. Saveliev},
     title = {Calculation of the number of states in binary {Markov} stochastic models},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {191--200},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2015_18_2_a6/}
}
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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/