Pogoruі, А. А. and Rodríguez-Dagnіno, Ramón М.
(2010)
Asymptotic expansion for transport processes in semi-Markov media.
Theor. Probability and Math. Statist. (83).
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 semigroup with the infinitesimal operator of the respective related bivariate process. Each regular and singular term can be calculated recursively.
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