A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution. (28th August 2011)

• Record Type: Journal Article
• Authors: Siu, D. P.; Ladde, G. S.
• Other Names: Anh V. V. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2011(2011)
• Publication Date: 2011-08-28
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2011/720614
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : 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.