Proofs of the martingale FCLT.
Propriété asymptotique d’un modèle statistique pour une chaîne de Markov à valeurs dans
Radius and profile of random planar maps with faces of arbitrary degrees.
Random real trees
We survey recent developments about random real trees, whose prototype is the Continuum Random Tree (CRT) introduced by Aldous in 1991. We briefly explain the formalism of real trees, which yields a neat presentation of the theory and in particular of the relations between discrete Galton-Watson trees and continuous random trees. We then discuss the particular class of self-similar random real trees called stable trees, which generalize the CRT. We review several important results concerning stable...
Random sets and their asymptotic measure
Random time changes for sock-sorting and other stochastic process limit theorems.
Random walk local time approximated by a brownian sheet combined with an independent brownian motion
Let ξ(k, n) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process ξ(k, n)−ξ(0, n) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.
Rates of convergence in the central limit theorem for empirical processes
Rates of convergence to the local time of a diffusion
Recent advances in invariance principles for stationary sequences.
Refinement of the Shannon-McMillan-Breiman theorem for some maps of an interval
Relationship between Extremal and Sum Processes Generated by the same Point Process
2000 Mathematics Subject Classification: Primary 60G51, secondary 60G70, 60F17.We discuss weak limit theorems for a uniformly negligible triangular array (u.n.t.a.) in Z = [0, ∞) × [0, ∞)^d as well as for the associated with it sum and extremal processes on an open subset S . The complement of S turns out to be the explosion area of the limit Poisson point process. In order to prove our criterion for weak convergence of the sum processes we introduce and study sum processes over explosion area....
Renormalization group of and convergence to the LISDLG process
The LISDLG process denoted by J(t) is defined in Iglói and Terdik [ESAIM: PS7 (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of J(t). It is shown that process J(t) has its own renormalization group and that J(t) can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations...
Renormalization group of and convergence to the LISDLG process
The LISDLG process denoted by is defined in Iglói and Terdik [ESAIM: PS 7 (2003) 23–86] by a functional limit theorem as the limit of ISDLG processes. This paper gives a more general limit representation of . It is shown that process has its own renormalization group and that can be represented as the limit process of the renormalization operator flow applied to the elements of some set of stochastic processes. The latter set consists of IGSDLG processes which are generalizations of the ISDLG...
Représentation du champ de fluctuation de diffusions indépendantes par le drap brownien
Rupture de modèles : loi asymptotique des statistiques de tests et des estimateurs du maximum de vraisemblance
Sample path large deviations principles for Poisson shot noise processes, and applications.
Scaling limit of the prudent walk.
Scaling limit of the random walk among random traps on ℤd
Attributing a positive value τx to each x∈ℤd, we investigate a nearest-neighbour random walk which is reversible for the measure with weights (τx), often known as “Bouchaud’s trap model.” We assume that these weights are independent, identically distributed and non-integrable random variables (with polynomial tail), and that d≥5. We obtain the quenched subdiffusive scaling limit of the model, the limit being the fractional kinetics process. We begin our proof by expressing the random walk as the...
Scaling of a random walk on a supercritical contact process
We prove a strong law of large numbers for a one-dimensional random walk in a dynamic random environment given by a supercritical contact process in equilibrium. The proof uses a coupling argument based on the observation that the random walk eventually gets trapped inside the union of space–time cones contained in the infection clusters generated by single infections. In the case where the local drifts of the random walk are smaller than the speed at which infection clusters grow, the random walk...