The stationary measure of the stochastic transport process with reflecting barriers in a semi-Markov environment
Author:
A. O. Pogoruĭ
Translated by:
Oleg Klesov
Journal:
Theor. Probability and Math. Statist. 74 (2007), 125-132
MSC (2000):
Primary 60K15; Secondary 90C40
DOI:
https://doi.org/10.1090/S0094-9000-07-00702-8
Published electronically:
July 5, 2007
MathSciNet review:
2336783
Full-text PDF Free Access
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Additional Information
Abstract: The stationary distribution is studied for the process described by stochastic evolution differential equations with reflecting barriers in a semi-Markov environment.
References
- V. S. Korolyuk, Stokhastichnī modelī sistem, “Libīd′”, Kiev, 1993 (Ukrainian, with Ukrainian summary). MR 1817881
- V. S. Korolyuk and A. V. Svishchuk, Polumarkovskie sluchaĭ nye èvolyutsii, “Naukova Dumka”, Kiev, 1992 (Russian, with English and Russian summaries). MR 1286045
- A. A. Pogoruĭ and A. F. Turbin, Estimation of stationary efficiency of a production line with two unreliable aggregates, Kibernetika i Sistemnyi Analiz 6 (2002), 35–42; English transl. in Cybernetics and Systems Analysis 38 (2002), no. 6, 823–829.
- A. F. Turbin and A. A. Pogoruĭ, Computation of stationary efficiency indices for inventory control systems with feedback, Intellectualization of systems for processing informational messages (Russian), Nats. Akad. Nauk Ukrainy, Inst. Mat., Kiev, 1995, pp. 191–204 (Russian, with Russian summary). MR 1365762
- Iosif I. Gikhman and Anatoli V. Skorokhod, The theory of stochastic processes. II, Classics in Mathematics, Springer-Verlag, Berlin, 2004. Translated from the Russian by S. Kotz; Reprint of the 1975 edition. MR 2058260
- Vladimir S. Korolyuk and Anatoly F. Turbin, Mathematical foundations of the state lumping of large systems, Mathematics and its Applications, vol. 264, Kluwer Academic Publishers Group, Dordrecht, 1993. Translated from the 1978 Russian original by V. V. Zayats and Y. A. Atanov and revised by the authors. MR 1281385
- A. N. Korlat, V. N. Kuznetsov, M. M. Novikov, and A. F. Turbin, Polumarkovskie modeli vosstanavlivaemykh sistem i sistem massovogo obsluzhivaniya, “Shtiintsa”, Kishinev, 1991 (Russian, with Russian summary). MR 1187752
References
- V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Lybid’, Kyiv, 1993; English transl., Kluwer Academic Publishers, Dordrecht, 1999. MR 1817881; MR 1753470 (2002b:60169)
- V. S. Korolyuk and A. V. Svishchuk, Semi-Markov Random Evolutions, Lybid’, Kyiv, 1992; English transl., Kluwer Academic Publishers, Dordrecht, 1995. MR 1286045 (95j:60143); MR 1472977 (98e:60145)
- A. A. Pogoruĭ and A. F. Turbin, Estimation of stationary efficiency of a production line with two unreliable aggregates, Kibernetika i Sistemnyi Analiz 6 (2002), 35–42; English transl. in Cybernetics and Systems Analysis 38 (2002), no. 6, 823–829.
- A. F. Turbin and A. A. Pogoruĭ, Computation of stationary efficiency indices for inventory control systems with feedback, Intellectualization of Systems for Processing Informational Messages, Nats. Akad. Nauk Ukrainy, Inst. Mat., Kyiv, 1995, pp. 191–204. (Russian) MR 1365762
- I. I. Gikhman and A. V. Skorokhod, The Theory of Stochastic Processes, vol. II, Nauka, Moscow, 1973; English transl., Springer-Verlag, New York–Heidelberg, 1975. MR 2058260 (2005a:60003)
- V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of the State Lumping of Large Systems, Kluwer Academic Publishers, Dordrecht, 1994. MR 1281385 (95e:60071)
- A. N. Korlat, V. N. Kuznetsov, M. M. Novikov, and A. F. Turbin, Semi-Markov Repairable Systems and Queuing Systems, Shtiintsa, Kishinev, 1991. (Russian) MR 1187752 (94e:60075)
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Additional Information
A. O. Pogoruĭ
Affiliation:
Department of Mathematics, Zhytomyr Pedagogical University, Velyka Berdychevs’ka Street, 40, 10008 Zhytomyr, Ukraine
Email:
pogor@zspu.edu.ua
Keywords:
Semi-Markov evolution,
infinitesimal operator,
stationary distribution
Received by editor(s):
December 23, 2003
Published electronically:
July 5, 2007
Article copyright:
© Copyright 2007
American Mathematical Society
