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Journal of Applied Mathematics
Volume 2015, Article ID 563060, 7 pages
http://dx.doi.org/10.1155/2015/563060
Research Article

Compensating Operator and Weak Convergence of Semi-Markov Process to the Diffusion Process without Balance Condition

Department of the System Analysis and Insurance and Financial Mathematics, Yuriy Fedkovych Chernivtsi National University, Universitetska Street 12, Chernivtsi 58012, Ukraine

Received 22 August 2015; Revised 8 November 2015; Accepted 9 November 2015

Academic Editor: Jinde Cao

Copyright © 2015 Igor V. Malyk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Weak convergence of semi-Markov processes in the diffusive approximation scheme is studied in the paper. This problem is not new and it is studied in many papers, using convergence of random processes. Unlike other studies, we used in this paper concept of the compensating operator. It enables getting sufficient conditions of weak convergence under the conditions on the local characteristics of output semi-Markov process.