Cutoff for samples of Markov chains
Cut-off for large sums of graphs
If is the combinatorial Laplacian of a graph, converges to a matrix with identical coefficients. The speed of convergence is measured by the maximal entropy distance. When the graph is the sum of a large number of components, a cut-off phenomenon may occur: before some instant the distance to equilibrium tends to infinity; after that instant it tends to . A sufficient condition for cut-off is given, and the cut-off instant is expressed as a function of the gap and eigenvectors of components....
Cutoff for samples of Markov chains
We study the convergence to equilibrium of samples of independent Markov chains in discrete and continuous time. They are defined as Markov chains on the fold Cartesian product of the initial state space by itself, and they converge to the direct product of copies of the initial stationary distribution. Sharp estimates for the convergence speed are given in terms of the spectrum of the initial chain. A cutoff phenomenon occurs in the sense that as tends to infinity, the total variation distance between...
Almost sure convergence of smoothing Dm-splines for noisy data.
Central limit theorem for hitting times of functionals of Markov jump processes
A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.
Central limit theorem for hitting times of functionals of Markov jump processes
A sample of i.i.d. continuous time Markov chains being defined, the sum over each component of a real function of the state is considered. For this functional, a central limit theorem for the first hitting time of a prescribed level is proved. The result extends the classical central limit theorem for order statistics. Various reliability models are presented as examples of applications.
Fast simulation for road traffic network
In this paper we present a method to perform fast simulation of large markovian systems. This method is based on the use of three concepts: Markov chain uniformization, event-driven dynamics, and modularity. An application of urban traffic simulation is presented to illustrate the performance of our approach.
Fast simulation for Road Traffic Network
In this paper we present a method to perform fast simulation of large Markovian systems. This method is based on the use of three concepts: Markov chain uniformization, event-driven dynamics, and modularity. An application of urban traffic simulation is presented to illustrate the performance of our approach.
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