86 citations · 383 across the 61 of their papers we have counts for
44 papers · 1 filter
Rate of convergence of the conditioned random walk towards the Brownian bridge
Laurent Decreusefond, Antonin Jacquet
We study the rate of convergence of two discrete processes towards the Brownian bridge: the random walk conditioned to be zero at time 2n and the empirical process which appears in…
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…
Optimal transport, determinantal point processes and the Bergman kernel
William Driot, Laurent Decreusefond
We study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Berg…
Stein's method for max-stable random vectors
Bruno Costacèque, Laurent Decreusefond
Motivated by the omnipresence of extreme value distributions in limit theorems involving extremes of random processes, we adapt Stein's method to include these laws as possible tar…
Random walks on simplicial complexes
Thomas Bonis, Laurent Decreusefond, Viet Chi Tran +1
The notion of Laplacian of a graph can be generalized to simplicial complexes and hypergraphs, and contains information on the topology of these structures. Even for a graph, the c…
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…
Rate of Convergence in the Functional Central Limit Theorem for Stable Processes
Lorick Huang, Laurent Decreusefond, Laure Coutin
In this article, we quantify the functional convergence of the rescaled random walk with heavy tails to a stable process.This generalizes the Generalized Central Limit Theorem for…
Invertibility of functionals of the Poisson process and applications
Laure Coutin, Laurent Decreusefond
Following previous investigations by {Ü}st{ü}nel [22] about the invertibility of some transformations on the Wiener space, we find some entropic conditions under which a random cha…
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…
Donsker's theorem in {Wasserstein}-1 distance
L. Coutin, Laurent Decreusefond
We compute the Wassertein-1 (or Kolmogorov-Rubinstein) distance between a random walk in and the Brownian motion. The proof is based on a new estimate of the Lipschitz modulu…
Stein's method and Papangelou intensity for Poisson or Cox process approximation
Laurent Decreusefond, Aurélien Vasseur
In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the…
Stein's method for diffusive limit of queueing processes
Eustache Besançon, E Besanç On, Laurent Decreusefond +1
Donsker Theorem is perhaps the most famous invariance principle result for Markov processes. It states that when properly normalized, a random walk behaves asymptotically like a Br…
Malliavin and dirichlet structures for independent random variables
Laurent Decreusefond, Hélène Halconruy
On any denumerable product of probability spaces, we construct a Malliavin gradient and then a divergence and a number operator. This yields a Dirichlet structure which can be show…
Stein's method for rough paths
Laure Coutin, Laurent Decreusefond
The original Donsker theorem says that a standard random walk converges in distribution to a Brownian motion in the space of continuous functions. It has recently been extended to…
Stochastic simulation of urban environments. Application to Path-loss in wireless systems
Thomas Courtat, Laurent Decreusefond, Phillipe Martins
We are interested in the assessment of electromagnetic Path-Loss in complex environments. The Path-loss is the attenuation function of the electromagnetic power at a distance $…
The Stein-Dirichlet-Malliavin method
Laurent Decreusefond
The Stein's method is a popular method used to derive upper-bounds of distances between probability distributions. It can be viewed, in certain of its formulations, as an avatar of…
A case study on regularity in cellular network deployment
Jean-Sébastien Gomez, Aurélien Vasseur, Anaïs Vergne +3
This paper aims to validate the -Ginibre point process as a model for the distribution of base station locations in a cellular network. The -Ginibre is a repulsive point proc…
Functional Poisson approximation in Kantorovich-Rubinstein distance with applications to U-statistics and stochastic geometry
Laurent Decreusefond, Matthias Schulte, Christoph Thäle
A Poisson or a binomial process on an abstract state space and a symmetric function acting on -tuples of its points are considered. They induce a point process on the target…
Higher order expansions via Stein method
Laure Coutin, Laurent Decreusefond
This paper is a sequel of \cite{CD:2012}. We show how to establish a functional Edgeworth expansion of any order thanks to the Stein method. We apply the procedure to the Brownian…
Disaster Recovery in Wireless Networks: A Homology-Based Algorithm
Anaïs Vergne, Ian Flint, Laurent Decreusefond +1
In this paper, we present an algorithm for the recovery of wireless networks after a disaster. Considering a damaged wireless network, presenting coverage holes or/and many disconn…
Random Abstract Simplicial Complexes Reduction
Anaïs Vergne, Laurent Decreusefond, Philippe Martins
Random abstract simplicial complex representation provides a mathematical description of wireless networks and their topology. In order to reduce the energy consumption in this typ…
Perfect Simulation of Determinantal Point Processes
Laurent Decreusefond, Ian Flint, Kah Choon Low
Determinantal point processes (DPP) serve as a practicable modeling for many applications of repulsive point processes. A known approach for simulation was proposed in \cite{Hough(…
Efficient simulation of the Ginibre point process
Laurent Decreusefond, Ian Flint, Anaïs Vergne
The Ginibre point process is one of the main examples of deter- minantal point processes on the complex plane. It forms a recurring model in stochastic matrix theory as well as in…
Moment formulae for general point processes
Laurent Decreusefond, Ian Flint
The goal of this paper is to generalize most of the moment formulae obtained in [Pri11]. More precisely, we consider a general point process μ, and show that the relevant quantitie…