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We provide complementary results for a family of models with dependence on their previous $k$-sum. Using a martingale-based approach, we establish a functional central limit theorem and analyze the limiting behavior of the center of mass.…

In this paper we establish some conditional limit theorems for some critical superprocesses $X=\{X_t, t\ge 0\}$. First we identify the rate of non-extinction. Then we show that, for a large class of functions $f$, conditioned on…

This paper addresses the following classical question: giving a sequence of identically distributed random variables in the domain of attraction of a normal law, does the associated linear process satisfy the central limit theorem? We study…

A Central Limit Theorem for non-commutative random variables is proved using the Lindeberg method. The theorem is a generalization of the Central Limit Theorem for free random variables proved by Voiculescu. The Central Limit Theorem in…

We present numerical results for a chemical reaction of colloidal particles which are transported by a laminar fluid and are focused by periodic obstacles in such a way that the two components are well mixed and consequently the chemical…

We prove a functional central limit theorem for subgraph counts in a dynamic version of the random connection model. To establish tightness, we develop a dynamic extension of the cumulant method.

We consider the stochastic heat equation whose solution is observed discretely in space and time. An asymptotic analysis of power variations is presented including the proof of a central limit theorem. It generalizes the theory from…

General Central limit theorem deals with weak limits (in type) of sums of row-elements of array random variables. In some situations as in the invariance principle problem, the sums may include only parts of the row-elements. For strictly…

In this paper, we establish some functional central limit theorems for a large class of general supercritical superprocesses with spatially dependent branching mechanisms satisfying a second moment condition. In the particular case when the…

In this paper, we consider a continuous-time Markov process and prove a local limit theorem for the integral of a time-inhomogeneous function of the process. One application is in the study of the fast-oscillating perturbations of linear…

In this note we prove that the speed of convergence of the workload of a L\'evy-driven queue to the quasi-stationary distribution is of order $1/t$. We identify also the Laplace transform of the measure giving this speed and provide some…

Results obtained several years ago using the high-resolution 93.3 keV M\"ossbauer resonance in $^{67}$ZnO and $\beta'$-brass have been reanalyzed with the notion that the clock hypothesis of Special Relativity Theory is not sufficient, but…

We characterize the convergence in distribution to a standard normal law for a sequence of multiple stochastic integrals of a fixed order with variance converging to 1. Some applications are given, in particular to study the limiting…

We obtain necessary and sufficient conditions for the regular variation of the variance of partial sums of functionals of discrete and continuous-time stationary Markov processes with normal transition operators. We also construct a class…

Central limit theorems and asymptotic properties of the minimum-contrast estimators of the drift parameter in linear stochastic evolution equations driven by fractional Brownian motion are studied. Both singular ($H < \frac{1}{2})$ and…

Consider the map $(x, y) \mapsto (x + \epsilon^{-\alpha} \sin (2\pi x) + \epsilon^{-1-\alpha}z, z + \epsilon \sin(2\pi x))$, which is conjugate to the Chirikov standard map with a large parameter. The parameter value $\alpha = 1$ is related…

In this paper, we propose a new approach to prove stability of non-linear discrete-time systems. After introducing the new concept of stability contractor, we show that the interval centred form plays a fundamental role in this context and…

In this paper, we derive a central limit theorem for collections of weakly correlated random variables indexed by discrete metric spaces, where the correlation decays in the distance of the indices. The correlation structure we study…

Let $\{{X}_k\}_{k\geq\mathbb{Z}}$ be a stationary sequence. Given $p\in(2,3]$ moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate $n^{p/2-1}$. For $p\geq4$, we also show a convergence rate of…

We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…