Asymptotic expansion for transport processes in semi-Markov media
Anatoliy A. Pogorui, Ramón M. Rodríguez‐Dagnino · Theory of Probability and Mathematical Statistics · 2011
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.