A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution
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 dy...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2011/720614 |
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| author | D. P. Siu G. S. Ladde |
| author_facet | D. P. Siu G. S. Ladde |
| author_sort | D. P. Siu |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-d5729afb04884383ac136068ccfa70f4 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-d5729afb04884383ac136068ccfa70f42025-02-03T01:12:12ZengWileyJournal of Probability and Statistics1687-952X1687-95382011-01-01201110.1155/2011/720614720614A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and DistributionD. P. Siu0G. S. Ladde1Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USADepartment of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USAIn 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.http://dx.doi.org/10.1155/2011/720614 |
| spellingShingle | D. P. Siu G. S. Ladde A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution Journal of Probability and Statistics |
| title | A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution |
| title_full | A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution |
| title_fullStr | A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution |
| title_full_unstemmed | A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution |
| title_short | A Multivariate Stochastic Hybrid Model with Switching Coefficients and Jumps: Solution and Distribution |
| title_sort | multivariate stochastic hybrid model with switching coefficients and jumps solution and distribution |
| url | http://dx.doi.org/10.1155/2011/720614 |
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