%0 Journal Article
%A Pogoruі, А. А.
%A Rodríguez-Dagnіno, Ramón М.
%D 2010
%F zu2:13404
%J Theor. Probability and Math. Statist.
%N 83
%T Asymptotic expansion for transport processes in semi-Markov media
%U http://eprints.zu.edu.ua/13404/
%X 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.