Convergence Rates in the Law of Large Numbers for Random Variables on Partially Ordered Sets.
Convergence results and sharp estimates for the voter model interfaces.
Convergence theorems for partial sums of arbitrary stochastic sequences.
Convergence theorems for set-valued conditional expectations
In this paper we prove two convergence theorems for set-valued conditional expectations. The first is a set-valued generalization of Levy’s martingale convergence theorem, while the second involves a nonmonotone sequence of sub -fields.
Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit. We also discuss...
Convergence to infinitely divisible distributions with finite variance for some weakly dependent sequences
We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the Gaussian and the purely non-Gaussian parts of the infinitely divisible limit. We also discuss...
Convergence to stable laws and a local limit theorem for stochastic recursions
We consider the random recursion , where x ∈ ℝ and (Mₙ,Qₙ,Nₙ) are i.i.d., Qₙ has a heavy tail with exponent α > 0, the tail of Mₙ is lighter and is smaller at infinity, than . Using the asymptotics of the stationary solutions we show that properly normalized Birkhoff sums converge weakly to an α-stable law for α ∈ (0,2]. The related local limit theorem is also proved.
Convergence to the brownian Web for a generalization of the drainage network model
We introduce a system of one-dimensional coalescing nonsimple random walks with long range jumps allowing paths that can cross each other and are dependent even before coalescence. We show that under diffusive scaling this system converges in distribution to the Brownian Web.
Convergence to zero and boundedness of operator-normed sums of random vectors with application to autoregression processes.
Convex concentration inequalities and forward-backward stochastic calculus.
Convexity of measures in certain convex cones in vector space ...-algebras.
Corrections : «Théorèmes limites pour les temps locaux d'un processus stable symétrique»
Corrigendum on "Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.
Corrigendum to “Stability of solutions of BSDEs with random terminal time”
This paper is a corrigendum to paper Toldo, ESAIM, P&S10 (2006) 141–163 where we study the stability of the solutions of Backward Stochastic Differential Equations (BSDE for short) with an almost surely finite random terminal time.
Counting and convergence in ergodic theory
Counting occurrences in almost sure limit theorems
Coupling a branching process to an infinite dimensional epidemic process***
Branching process approximation to the initial stages of an epidemic process has been used since the 1950's as a technique for providing stochastic counterparts to deterministic epidemic threshold theorems. One way of describing the approximation is to construct both branching and epidemic processes on the same probability space, in such a way that their paths coincide for as long as possible. In this paper, it is shown, in the context of a Markovian model of parasitic infection, that coincidence...
Courte démonstration du théorème ergodique sur-additif
Covariance inequalities for strongly mixing processes
Cramer Type Large Deviations for Studentized U-Statistics.