| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1155182 | Statistics & Probability Letters | 2008 | 7 Pages |
Abstract
We study the time evolution of an increasing stochastic process governed by a first-order stochastic differential system. This defines a particular piecewise deterministic Markov process (PDMP). We consider a Markov renewal process (MRP) associated to the PDMP and its Markov renewal equation (MRE) which is solved in order to obtain a closed-form solution of the transition function of the PDMP. It is then applied in the framework of survival analysis to evaluate the reliability function of a given system. We give a numerical illustration and we compare this analytical solution with the Monte Carlo estimator.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Julien Chiquet, Nikolaos Limnios,