On modulated random measures.
On self-optimizing control of Markov processes
On the large deviations of a class of modulated additive processes
We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn...
On the large deviations of a class of modulated additive processes
We prove that the large deviation principle holds for a class of processes inspired by semi-Markov additive processes. For the processes we consider, the sojourn times in the phase process need not be independent and identically distributed. Moreover the state selection process need not be independent of the sojourn times. We assume that the phase process takes values in a finite set and that the order in which elements in the set, called states, are visited is selected stochastically. The sojourn...
On the number of collisions in lambda-coalescents.
On truncations for weakly ergodic inhomogeneous birth and death processes
Prévision de la demande de soins à partir d'un système d'information décentralisé
Relative stability and weak convergence in non-decreasing stochastically monotone Markov chains.
Reliability modeling of fault tolerant control systems
This paper proposes a novel approach to reliability evaluation for active Fault Tolerant Control Systems (FTCSs). By introducing a reliability index based on the control performance and hard deadline, a semi-Markov process model is proposed to describe system operation for reliability evaluation. The degraded performance of FTCSs in the presence of imperfect Fault Detection and Isolation (FDI) is reflected by semi-Markov states. The semi-Markov kernel, the key parameter of the process, is determined...
Renewal theorem for a system of renewal equations
Semi-groupes et mesures invariantes pour les processus semi-markoviens à espace d'état quelconque
Semi-Markov control processes with non-compact action spaces and discontinuous costs
We establish the average cost optimality equation and show the existence of an (ε-)optimal stationary policy for semi-Markov control processes without compactness and continuity assumptions. The only condition we impose on the model is the V-geometric ergodicity of the embedded Markov chain governed by a stationary policy.
Semi-Markov processes for reliability studies
Semi-Markov processes for reliability studies
We study the evolution of a multi-component system which is modeled by a semi-Markov process. We give formulas for the avaibility and the reliability of the system. In the r-positive case, we prove that the quasi-stationary probability on the working states is the normalised left eigenvector of some computable matrix and that the asymptotic failure rate is equal to the absolute value of the convergence parameter r.
Semi-Markov reliability models with recurrence times and credit rating applications.
Semi-Markov switches
Single-use reliability computation of a semi-Markovian system
Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first...
Stochastic integral by a semi-Markov process of diffusion type.
The failure rate in reliability: Approximations and bounds.
The failure rate in reliability. Numerical treatment.