Journal of Probability and Statistics
Volume 2011 (2011), Article ID 720614, 20 pages
Research Article

A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution

Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA

Received 9 May 2011; Accepted 7 June 2011

Academic Editor: V. V. Anh

Copyright © 2011 D. P. Siu and G. S. Ladde. 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.


In this work, a class of multidimensional stochastic hybrid dynamic models is studied. The system under investigation is a first-order linear nonhomogeneous system of Itô-Doob type stochastic differential equations with switching coefficients. The switching of the system is governed by a discrete dynamic which is monitored by a non-homogeneous Poisson process. Closed-form solutions of the systems are obtained. Furthermore, the major part of the work is devoted to finding closed-form probability density functions of the solution processes of linear homogeneous and Ornstein-Uhlenbeck type systems with jumps.