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Asymptotic expansion for transport processes in semi-Markov media
Authors:
A. A. Pogorui and Ramón M. Rodríguez-Dagnino
Original publication:
Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal:
Theor. Probability and Math. Statist. 83 (2011), 127-134
MSC (2010):
Primary 60J25; Secondary 35C20
Posted:
February 2, 2012
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Abstract: In this paper we study asymptotic expansions for a solution of the singularly perturbed equation for a functional of a semi-Markov random evolution on the line. By using the method for solutions of singularly perturbed equations, we obtain the solution in the form of a series of regular and singular terms. The first regular term satisfies a diffusion-type equation, and the first singular term is a semi-group with the infinitesimal operator of the respective related bivariate process. Each regular and singular term can be calculated recursively.
References
- 1.
V. S. Korolyuk and V. V. Korolyuk, Stochastic Models of Systems, Kluwer Academic Publishers, 1998. MR 1753470 (2002b:60169)
- 2.
V. S. Korolyuk and A. V. Swishchuk, Evolution of Systems in Random Media, CRC Press, Boca Raton, FL, U.S.A., 1995. MR 1413300 (98g:60116)
- 3.
I. I. Gikhman and A. V. Skorokhod, The theory of Stochastic Processes, vol. 2, Springer-Verlag, New York, 1975. MR 0375463 (51:11656)
- 4.
V. S. Korolyuk and A. F. Turbin, Markov Renewal Processes in System Reliability Problems, Naukova Dumka, Kiev, 1982. (Russian) MR 695006 (85e:60095)
- 5.
V. S. Korolyuk and A. F. Turbin, Mathematical Foundations of the State Lumping of Large Systems, Kluwer Academic Publishers, 1993. MR 1281385 (95e:60071)
- 6.
A. B. Vasil'eva and V. F. Butuzov, Asymptotic Methods in the Theory of Singular Perturbations, Vysshaya Shkola, Moscow, 1990. (Russian) MR 1108181 (92i:34072)
- 7.
S. Albeverio, V. S. Koroliuk, and I. V. Samoilenko, Asymptotic
expansion of semi-Markov random evolutions, Stochastics
81 (2009), no. 5, 477–502. MR 2569263
(2010k:60311), http://dx.doi.org/10.1080/17442500802432020
- 8.
I. V. Samoilenko, Asymptotic expansion of Markov random evolution, Ukrainian Mathematical Bulletin 3 (2006), no. 3, 394-407. MR 2330681 (2008d:60098)
- 9.
Anatoly A. Pogorui, Asymptotic expansion for the distribution of a
Markovian random motion, Random Oper. Stoch. Equ. 17
(2009), no. 2, 189–196. MR 2560865
(2010i:60217), http://dx.doi.org/10.1515/ROSE.2009.013
- 10.
M. A. Pinsky, Lectures on Random Evolutions, World Scientific Publishing, 1991. MR 1143780 (93b:60160)
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Additional Information
A. A. Pogorui
Affiliation:
Zhytomyr State Ivan Franko University, Velyka Berdychivs’ka St. 40, Zhytomyr 10008, Ukraine
Email:
pogor@zu.edu.ua
Ramón M. Rodríguez-Dagnino
Affiliation:
Centro de Electrónica y Telecomunicaciones, ITESM, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, N.L., México
Email:
rmrodrig@itesm.mx
DOI:
http://dx.doi.org/10.1090/S0094-9000-2012-00846-6
PII:
S 0094-9000(2012)00846-6
Keywords:
Asymptotic expansion,
semi-Markov,
random evolution,
singular perturbed equation
Received by editor(s):
20/OCT/2009
Posted:
February 2, 2012
Additional Notes:
We thank ITESM, Campus Monterrey, through the Research Chair in Telecommunications, for the support provided in the development of this work
Article copyright:
© Copyright 2012 American Mathematical Society
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