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

Abstract EN

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.