The approximate Euler method for Lévy driven stochastic differential equations
The Dispersion of the Hammersley Sequence in the Unit Square.
The failure of orthogonality under nonstationarity: should we care about it?
The Gauss center research in multiscale scientific computation.
The inverse of the star-discrepancy depends linearly on the dimension
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-Smirnov distance as criterion of choice of estimators with application to the first order auto-regressive case : a Monte Carlo study
The N-Armed Bandit with Unimodal Structure.
The time needed for estimation of a functional by the Monte Carlo method
Theoretical and numerical comparison of some sampling methods for molecular dynamics
The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the...
Three Digit Accurate Multiple Normal Probabilities.
Trend to equilibrium and particle approximation for a weakly selfconsistent Vlasov-Fokker-Planck equation
We consider a Vlasov-Fokker-Planck equation governing the evolution of the density of interacting and diffusive matter in the space of positions and velocities. We use a probabilistic interpretation to obtain convergence towards equilibrium in Wasserstein distance with an explicit exponential rate. We also prove a propagation of chaos property for an associated particle system, and give rates on the approximation of the solution by the particle system. Finally, a transportation inequality...