On the integrability of Banach space valued Walsh polynomials
On the Integrability of the Limit of a Supercritical Branching Process
On the invariant measure of the random difference equation Xn = AnXn−1 + Bn in the critical case
We consider the autoregressive model on ℝd defined by the stochastic recursion Xn = AnXn−1 + Bn, where {(Bn, An)} are i.i.d. random variables valued in ℝd× ℝ+. The critical case, when , was studied by Babillot, Bougerol and Elie, who proved that there exists a unique invariant Radon measureν for the Markov chain {Xn}. In the present paper we prove that the weak limit of properly dilated measure ν exists and defines a homogeneous measure on ℝd ∖ {0}.
On the joining of sticky brownian motion
On the joint distribution of the maximum and its location for a linear diffusion
On the Kantorovich-Rubinstein maximum principle for the Fortet-Mourier norm
A new version of the maximum principle is presented. The classical Kantorovich-Rubinstein principle gives necessary conditions for the maxima of a linear functional acting on the space of Lipschitzian functions. The maximum value of this functional defines the Hutchinson metric on the space of probability measures. We show an analogous result for the Fortet-Mourier metric. This principle is then applied in the stability theory of Markov-Feller semigroups.
On the left tail asymptotics for the limit law of supercritical Galton–Watson processes in the Böttcher case
Under a well-known scaling, supercritical Galton–Watson processes Z converge to a non-degenerate non-negative random limit variable W. We are dealing with the left tail (i.e. close to the origin) asymptotics of its law. In the Böttcher case (i.e. if always at least two offspring are born), we describe the precise asymptotics exposing oscillations (Theorem 1). Under a reasonable additional assumption, the oscillations disappear (Corollary 2). Also in the Böttcher case, we improve a recent lower deviation...
On the lengths of excursions of some Markov processes
On the Lévy transformation of brownian motions and continuous martingales
On the limit distributions of kth order statistics for semi-pareto processes
Asymptotic properties of the kth largest values for semi-Pareto processes are investigated. Conditions for convergence in distribution of the kth largest values are given. The obtained limit laws are represented in terms of a compound Poisson distribution.
On the local time density of the reflecting Brownian bridge.
On the Markov chain central limit theorem.
On the martingale problem for super-brownian motion
On the martingales obtained by an extension due to Saisho, Tanemura and Yor of Pitman's theorem
On the Maximum of a Branching Process Conditioned on the Total Progeny
The maximum M of a critical Bienaymé-Galton-Watson process conditioned on the total progeny N is studied. Imbedding of the process in a random walk is used. A limit theorem for the distribution of M as N → ∞ is proved. The result is trasferred to the non-critical processes. A corollary for the maximal strata of a random rooted labeled tree is obtained.
On the maximum of a diffusion process in a drifted brownian environment
On the mean speed of convergence of empirical and occupation measures in Wasserstein distance
In this work, we provide non-asymptotic bounds for the average speed of convergence of the empirical measure in the law of large numbers, in Wasserstein distance. We also consider occupation measures of ergodic Markov chains. One motivation is the approximation of a probability measure by finitely supported measures (the quantization problem). It is found that rates for empirical or occupation measures match or are close to previously known optimal quantization rates in several cases. This is notably...
On the moments of hitting times for random walks on trees.
On the noncoalescence of a two point brownian motion reflecting on a circle
On the number of collisions in lambda-coalescents.