Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 549651, 12 pages
doi:10.1155/2011/549651
Research Article

Existence and Uniqueness Theorem for Stochastic Differential Equations with Self-Exciting Switching

1Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai 264209, China
2School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received 5 December 2010; Accepted 27 March 2011

Academic Editor: Xue He

Copyright © 2011 Guixin Hu and Ke Wang. 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

We introduce a new kind of equation, stochastic differential equations with self-exciting switching. Firstly, we give some preliminaries for this kind of equation, and then, we get the main results of our paper; that is, we gave the sufficient condition which can guarantee the existence and uniqueness of the solution.