Geodesic
Piecewise linear Markov chains and analysis of their stability
Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 345-357

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Piecewise linear functions and piecewise linear operators are defined, some of their properties are studied. A class of piecewise linear Markov chains is introduced by means of the notion of piecewise linear operator. A stability problem for these chains is solved by virtue of the Lyapunov function method. Some examples of piecewise linear Markov chains describing queueing systems are considered. 
@article{TVP_1975_20_2_a7,
     author = {G. Sh. Tsitsiashvili},
     title = {Piecewise linear {Markov} chains and analysis of their stability},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {345--357},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a7/}
}
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G. Sh. Tsitsiashvili. Piecewise linear Markov chains and analysis of their stability. Teoriâ veroâtnostej i ee primeneniâ, Tome 20 (1975) no. 2, pp. 345-357. http://geodesic.mathdoc.fr/item/TVP_1975_20_2_a7/