Conjugate transforms and limit theorems for semigroups
Constructions of smooth and analytic cocycles over irrational circle rotations
We define a class of step cocycles (which are coboundaries) for irrational rotations of the unit circle and give conditions for their approximation by smooth and real analytic coboundaries. The transfer functions of the approximating (smooth and real analytic) coboundaries are close (in the supremum norm) to the transfer functions of the original ones. This result makes it possible to construct smooth and real analytic cocycles which are ergodic, ergodic and squashable (see [Aaronson, Lemańczyk,...
Convergence en loi des H-variations d'un processus gaussien stationnaire sur R
Convergence en loi pour la topologie de Skorohod éclatée du processus empirique multidimensionnel normalisé tronqué éclaté et corrigé
Convergence in distribution for subset counts between random sets.
Convergence in fractional models and applications.
Convergence in mean of weighted sums of -compactly uniformly integrable random elements in Banach spaces.
Convergence in r-Mean of Normalized Partial Sums in a Separable Banach Space.
Convergence of a branching type recursion
Convergence of a Branching Type Recursion with Non-Stationary Immigration.
Convergence of conditional expectations
Convergence of lattice trees to super-Brownian motion above the critical dimension.
Convergence of stopped sums of weakly dependent random variables.
Convergence of weighted linear process for -mixing random variables.
Convergence pour les processus empiriques éclatés
Convergence rate of the distributions of normalized maximum likelihood estimators for irregular parametric families.
Convergence Rates in the Law of Large Numbers for Random Variables on Partially Ordered Sets.
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.