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

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  • D. P. Siu
  • G. S. Ladde

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.

Suggested Citation

  • D. P. Siu & G. S. Ladde, 2011. "A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution," Journal of Probability and Statistics, Hindawi, vol. 2011, pages 1-20, August.
    • Handle: RePEc:hin:jnljps:720614
    DOI: 10.1155/2011/720614
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