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63 papers · 1 filter
Stein's functional method for weakly dependent random variables
Laure Coutin, Sérigné Darou Kebe, Laurent Decreusefond
This article extends Stein's functional method to establish explicit rates of convergence in the Wasserstein-1 distance for Donsker's invariance principle under weak dependence. Ou…
Quantitative Limit Theorems for Cox-Poisson and Cox-Binomial Point Processes
Hamza Adrat, Laurent Decreusefond
This paper establishes quantitative limit theorems for two classes of Cox point processes, quantifying their convergence to a Poisson point process (PPP). We employ Stein's method…
Malliavin structure for conditionally independent random variables
Laurent Decreusefond, Christophe Vuong
On any denumerable product of probability spaces, we extend the discrete Malliavin structure for conditionally independent random variables. As a consequence, we obtain the chaos d…
Long run convergence of discrete-time interacting particle systems of the McKean-Vlasov type
Pascal Bianchi, Walid Hachem, Victor Priser
We consider a discrete-time system of n coupled random vectors, a.k.a. interacting particles. The dynamics involve a vanishing step size, some random centered perturbations, and a…
Diffusive limits of Lipschitz functionals of Poisson measures
Eustache Besançon, Laure Coutin, Laurent Decreusefond +1
Continuous Time Markov Chains, Hawkes processes and many other interesting processes can be described as solution of stochastic differential equations driven by Poisson measures. P…
Hidden regular variation for point processes and the single/multiple large point heuristic
Clément Dombry, Charles Tillier, Olivier Wintenberger
We consider regular variation for marked point processes with independent heavy-tailed marks and prove a single large point heuristic: the limit measure is concentrated on the cone…