Geodesic
Simple stochastic models of fractures
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 97-106.

Voir la notice de l'article provenant de la source Math-Net.Ru

Stochastic Markov models describe various natural and technical processes. They are often used in various fields. In particular, there are considered Markov models with discrete time and few states. In particular cases, such models make it possible to implement efficient computations. The article deals with special models with two, four, and eight states as well as the processes with hydraulic fracturing and the development of a wavefront.
Keywords: stochastic modeling, Markov models, finite Markov chain, crack, probability, mean. 
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     title = {Simple stochastic models of fractures},
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L. Ya. Savel'ev. Simple stochastic models of fractures. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 97-106. http://geodesic.mathdoc.fr/item/SJIM_2014_17_2_a9/

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

[2] Savelev L., Balakin S., Konechnye markovskie tsepi i serii (teoriya i prilozheniya), Lap Lambert Acad. Publ., Saarbrücken, 2012

[3] Feller V., Vvedenie v teoriyu veroyatnostei i ee prilozheniya, v. 1–2, Mir, M., 1984 | Zbl

[4] Savelev L., Balakin S., “Nekotorye primeneniya stokhasticheskoi teorii serii”, Sib. zhurn. industr. matematiki, 15:3(51) (2012), 111–123 | MR

[5] Kanevskaya R. D., Matematicheskoe modelirovanie razrabotki mestorozhdenii nefti i gaza s primeneniem gidravlicheskogo razryva plasta, Nedra-Biznestsentr, M., 1999

[6] Aizenberg-Stepanenko M. V., Sher E. N., “Modelirovanie volnovykh yavlenii v strukturirovannykh sredakh”, Fiz. mezomekhanika, 10:1 (2007), 47–57