87 research outputs found
Nonparametric estimation of renewal processes from count data.
International audienceno abstrac
Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
International audienceIn the reliability theory, the availability of a component, characterized by non constant failure and repair rates, is obtained, at a given time, thanks to the computation of the marginal distributions of a semi-Markov process. These measures are shown to satisfy classical transport equations, the approximation of which can be done thanks to a finite volume method. Within a uniqueness result for the continuous solution, the convergence of the numerical scheme is then proven in the weak measure sense, and some numerical applications, which show the efficiency and the accuracy of the method, are given
A finite-volume scheme for dynamic reliability models
International audienceIn a model arising in the dynamic reliability study of a system, the probability of the state of the system is completely described by the Chapman-Kolmogorov equations, which are scalar linear hyperbolic partial differential equations coupled by their right-hand side, the solution of which are probability measures. We propose in this paper a finite-volume scheme to approximate these measures. We show, thanks to the proof of the tightness of the approximate solution, that the conservation of the probability mass leads to a compactness property. The convergence of the scheme is then obtained in the space of continuous functions with respect to the time variable, valued in the set of probability measures on R-d. We finally show on a numerical example the accuracy and efficiency of the approximation method
From urn models to zero-range processes: statics and dynamics
The aim of these lecture notes is a description of the statics and dynamics
of zero-range processes and related models. After revisiting some conceptual
aspects of the subject, emphasis is then put on the study of the class of
zero-range processes for which a condensation transition arises.Comment: Lecture notes for the Luxembourg Summer School 200
Nonequilibrium Statistical Mechanics of the Zero-Range Process and Related Models
We review recent progress on the zero-range process, a model of interacting
particles which hop between the sites of a lattice with rates that depend on
the occupancy of the departure site. We discuss several applications which have
stimulated interest in the model such as shaken granular gases and network
dynamics, also we discuss how the model may be used as a coarse-grained
description of driven phase-separating systems. A useful property of the
zero-range process is that the steady state has a factorised form. We show how
this form enables one to analyse in detail condensation transitions, wherein a
finite fraction of particles accumulate at a single site. We review
condensation transitions in homogeneous and heterogeneous systems and also
summarise recent progress in understanding the dynamics of condensation. We
then turn to several generalisations which also, under certain specified
conditions, share the property of a factorised steady state. These include
several species of particles; hop rates which depend on both the departure and
the destination sites; continuous masses; parallel discrete-time updating;
non-conservation of particles and sites.Comment: 54 pages, 9 figures, review articl
A sequential condition-based repair/replacement policy with non-periodic inspections for a system subject to continuous wear
Approximation of the marginal distributions of a semi-Markov process using a finite volume scheme
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