Convergence rate of the distributions of normalized maximum likelihood estimators for irregular parametric families.
Convergence rates for probabilities of moderate deviations for multidimensionally indexed random variables.
Convergence rates for quadratic forms of random variables
Convergence rates for the full gaussian rough paths
Under the key assumption of finite -variation, , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), resp. , we recover and extend the respective results of (Trans. Amer. Math. Soc.361 (2009) 2689–2718) and (Ann. Inst. Henri Poincasé Probab. Stat.48(2012) 518–550). In particular, we establish an a.s. rate , any , for Wong–Zakai and Milstein-type...
Convergence rates for weighted sums of random variables with random indices
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.
Convergence uniforme à distance finie de mesures signées
Convergences de Martingales a valeurs Vectorielles
Convergent Nonnegative Matrices and Iterative Methods for Consistent Linear Systems.
Convergent rearrangements of series of vector-valued functions.
Convex analysis for sets of local martingales measures
Convex concentration inequalities and forward-backward stochastic calculus.