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.
| Original language | English |
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| Pages (from-to) | 1397-1403 |
| Number of pages | 7 |
| Journal | Statistics and Probability Letters |
| Volume | 78 |
| Issue number | 12 |
| DOIs | |
| Publication status | Published - 1 Sept 2008 |
| Externally published | Yes |