Related papers: A functional central limit theorem for the empiric…

The central limit theorem of martingales is the fundamental tool for studying the convergence of stochastic processes. The central limit theorem and functional central limit theorem are obtained for martingale like random variables under…

Motivated by applications to the study of depth functions for tree-indexed random variables generated by point processes, we describe functional limit theorems for the intensity measure of point processes. Specifically, we establish uniform…

In this work, a generalised version of the central limit theorem is proposed for nonlinear functionals of the empirical measure of i.i.d. random variables, provided that the functional satisfies some regularity assumptions for the…

Let $(U_n(t))_{t\in\R^d}$ be the empirical process associated to an $\R^d$-valued stationary process $(X_i)_{i\ge 0}$. We give general conditions, which only involve processes $(f(X_i))_{i\ge 0}$ for a restricted class of functions $f$,…

In this paper we study supercritical super-OU processes with general branching mechanisms satisfying a second moment condition. We establish central limit theorems for the super-OU processes. In the small and crtical branching rate cases,…

This article considers multivariate linear processes whose components are either short- or long-range dependent. The functional central limit theorems for the sample mean and the sample autocovariances for these processes are investigated,…

The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point-wise ergodic conditions studied in…

This paper deals with Poisson processes on an arbitrary measurable space. Using a direct approach, we derive formulae for moments and cumulants of a vector of multiple Wiener-It\^o integrals with respect to the compensated Poisson process.…

We prove central limit theorems (CLT) for empirical processes of extreme values cluster functionals as in Drees and Rootz\'en (2010). We use coupling properties enlightened for Dedecker \& Prieur's $\tau-$dependence coefficients in order to…

In this short communication we present a (functional) central limit theorem for the idle process of a one-sided reflected Ornstein-Uhlenbeck proces.

Under an appropriate regular variation condition, the affinely normalized partial sums of a sequence of independent and identically distributed random variables converges weakly to a non-Gaussian stable random variable. A functional version…

We introduce and investigate a new notion of the theory of approximation-the so-called degenerate approximation, i.e. approximation of the function of two (and more) variables (kernel) by means of degenerate function (kernel). We apply…

For a $d\times d$ expanding matrix $A$, we investigate randomness of the sequence $\{A^k x\}$ and prove the central limit theorem for $\sum f(A^k x)$ where $f$ is a periodic function with a mild regularity condition.

We provide an abstract multivariate central limit theorem with the Lindeberg-type error bounded in terms of Lipschitz functions (Wasserstein 1-distance) or functions with bounded second or third derivatives. The result is proved by means of…

In this paper we prove a criterion of convergence in distribution in Skorokhod space. We apply this criterion to some special Levy processes and obtain almost-sure versions of limit theorems for these processes.

We establish precise bounds on cumulants for a rather general class of non-linear geometric functionals satisfying the stabilization property under a simple, stationary (marked) point process admitting fast decay of its correlation…

We prove a functional limit theorem for vector-valued functionals of the fractional Ornstein-Uhlenbeck process, providing the foundation for the fluctuation theory of slow/fast systems driven by such a noise. Our main contribution is on the…

This paper aims to establish a central limit theorem for Markov processes conditioned not to be absorbed under a very general assumption on quasi-stationarity for the underlying process. To do so, a central limit theorem has been…

In this paper, we prove maximal inequalities and study the functional central limit theorem for the partial sums of linear processes generated by dependent innovations. Due to the general weights, these processes can exhibit long-range…

We use the circle method to evaluate the behavior of limit-periodic functions on primes. For those limit-periodic functions that satisfy a kind of Barban-Davenport-Halberstam condition and whose singular series converge fast enough, we can…