The joint law of ages and residual lifetimes for two schemes of nested regenerative sets.
The Kendall theorem and its application to the geometric ergodicity of Markov chains
We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of...
The Kolmogorov equation in the stochastic fragmentation theory and branching processes with infinite collection of particle types.
The large-scale limit of Dyson's hierarchical vector valued model at low temperatures. The non-gaussian case. Part I : limit theorem for the average spin
The large-scale limit of Dyson's hierarchical vector-valued model at low temperatures. The non-gaussian case. Part II : description of the large-scale limit
The law of large numbers for ballistic, multi-dimensional random walks on random lattices with correlated sites
The logarithmic Sobolev constant of Kawasaki dynamics under a mixing condition revisited
The longtime behavior of branching random walk in a catalytic medium.
The , queue with preemptive priority.
The queue with queue length dependent service times.
The Markov process of total spins
The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary
The mass of sites visited by a random walk on an infinite graph.
The metastability threshold for modified bootstrap percolation in dimensions.
The M/G/1 retrial queue: an information theoretic approach.
In this paper, we give a survey of the use of information theoretic techniques for the estimation of the main performance characteristics of the M/G/1 retrial queue. We focus on the limiting distribution of the system state, the length of a busy period and the waiting time. Numerical examples are given to illustrate the accuracy of the maximum entropy estimations when they are compared versus the classical solutions.
The M/M/1 queue is Bernoulli
The classical output theorem for the M/M/1 queue, due to Burke (1956), states that the departure process from a stationary M/M/1 queue, in equilibrium, has the same law as the arrivals process, that is, it is a Poisson process. We show that the associated measure-preserving transformation is metrically isomorphic to a two-sided Bernoulli shift. We also discuss some extensions of Burke's theorem where it remains an open problem to determine if, or under what conditions, the analogue of this result...
The Modified M/G/1 queue
The MX/M/1 queue with working breakdown
In this paper, we consider a batch arrival MX/M/1 queue model with working breakdown. The server may be subject to a service breakdown when it is busy, rather than completely stoping service, it will decrease its service rate. For this model, we analyze a two-dimensional Markov chain and give its quasi upper triangle transition probability matrix. Under the system stability condition, we derive the probability generating function (PGF) of the stationary queue length, and then obtain its stochastic...
The ODE method for some self-interacting diffusions on ℝd
The aim of this paper is to study the long-term behavior of a class of self-interacting diffusion processes on ℝd. These are solutions to SDEs with a drift term depending on the actual position of the process and its normalized occupation measure μt. These processes have so far been studied on compact spaces by Benaïm, Ledoux and Raimond, using stochastic approximation methods. We extend these methods to ℝd, assuming a confinement potential satisfying some conditions. These hypotheses on the confinement...
The one dimensional annealed δ-Lyapounov exponent