This paper investigates the rate of occurrence of failures (ROCOF) of finite state semi-Markov systems. Firstly, a formula for evaluating the ROCOF for semi-Markov systems is derived. As a consequence of this result, we derive the ROCOF of Markov systems as well as the ROCOF of the alternating...

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...

The aim of this paper is to introduce a general bootstrap by exchangeable weight random variables for empirical estimators of the semi-Markov kernels and of the conditional transition probabilities for semi-Markov processes with countable state space. Asymptotic properties of these generalized...

In this paper we consider the problem of an insurance company where the wealth of the insurer is described by a Cramér-Lundberg process. The insurer is allowed to invest in a risky asset with stochastic volatility subject to the influence of an economic factor and the remaining surplus in a...