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Theory of Probability and Mathematical Statistics

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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
Published electronically: February 2, 2012
MathSciNet review: 2768853
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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.

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Additional Information

A. A. Pogorui
Affiliation: Zhytomyr State Ivan Franko University, Velyka Berdychivs’ka St. 40, Zhytomyr 10008, Ukraine

Ramón M. Rodríguez-Dagnino
Affiliation: Centro de Electrónica y Telecomunicaciones, ITESM, E. Garza Sada 2501 Sur, C.P. 64849, Monterrey, N.L., México

Keywords: Asymptotic expansion, semi-Markov, random evolution, singular perturbed equation
Received by editor(s): October 20, 2009
Published electronically: 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