Asymptotic expansion for transport processes in semi-Markov media
Authors:
A. A. Pogorui and Ramón M. Rodríguez-Dagnino
Journal:
Theor. Probability and Math. Statist. 83 (2011), 127-134
MSC (2010):
Primary 60J25; Secondary 35C20
DOI:
https://doi.org/10.1090/S0094-9000-2012-00846-6
Published electronically:
February 2, 2012
MathSciNet review:
2768853
Full-text PDF Free Access
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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
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References
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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
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
