相关论文: Central limit theorems for Poisson hyperplane tess…

In this paper, we establish a version of the central limit theorem for Markov-Feller continuous time processes (with a Polish state space) that are exponentially ergodic in the bounded-Lipschitz distance and enjoy a continuous form of the…

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,…

Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…

A central limit theorem is established for a sum of random variables belonging to a sequence of random fields. The fields are assumed to have zero mean conditional on the past history and to satisfy certain conditional $\alpha$-mixing…

We consider the Fleming--Viot particle system associated with a continuous-time Markov chain in a finite space. Assuming irreducibility, it is known that the particle system possesses a unique stationary distribution, under which its…

This paper establishes a central limit theorem and an invariance principle for a wide class of stationary random fields under natural and easily verifiable conditions. More precisely, we deal with random fields of the form $X_k =…

For a stationary Poisson hyperplane tessellation $X$ in ${\mathbb R}^d$, whose directional distribution satisfies some mild conditions (which hold in the isotropic case, for example), it was recently shown that with probability one every…

Consider a measure $\mu_\lambda = \sum_x \xi_x \delta_x$ where the sum is over points $x$ of a Poisson point process of intensity $\lambda$ on a bounded region in $d$-space, and $\xi_x$ is a functional determined by the Poisson points near…

We use a functional analogue of the quantile function for probability measures on $\mathbb{R}^d$ to characterize a novel limit Poisson point process for radially recentred and rescaled random vectors under a radial-directional…

The local (central) limit theorem precisely describes the behavior of iterated convolution powers of a probability distribution on the $d$-dimensional integer lattice, $\mathbb{Z}^d$. Under certain mild assumptions on the distribution, the…

Let $X_1,\ldots,X_n$ be a sequence of independent random points in $\mathbb{R}^d$ with common Lebesgue density $f$. Under some conditions on $f$, we obtain a Poisson limit theorem, as $n \to \infty$, for the number of large probability…

Let K be a convex set in R d and let K $\lambda$ be the convex hull of a homogeneous Poisson point process P $\lambda$ of intensity $\lambda$ on K. When K is a simple polytope, we establish scaling limits as $\lambda$ $\rightarrow$ $\infty$…

We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…

In this paper we prove a quantitative central limit theorem for the area of uniform random disc-polygons in smooth convex discs whose boundary is $C^2_+$. We use Stein's method and the asymptotic lower bound for the variance of the area…

Let $K_\lambda^d$ be the convex hull of the intersection of the homogeneous Poisson point process of intensity $\lambda$ in $\mathbb{R}^d$, $d \ge 2$, with the Euclidean unit ball $\mathbb{B}^d$. In this paper, we study the asymptotic…

We prove a Central Limit Theorem for the finite dimensional distributions of the displacement for the 1D self-repelling diffusion which solves \begin{equation*} dX_t =dB_t -\big(G'(X_t)+ \int_0^t F'(X_t-X_s)ds\big)dt, \end{equation*} where…

We consider a finite sequence of random points in a finite domain of a finite-dimensional Euclidean space. The points are sequentially allocated in the domain according to a model of cooperative sequential adsorption. The main peculiarity…

This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634--658,…

This paper establishes central limit theorems for Polyak-Ruppert averaged Q-learning under asynchronous updates. We prove a non-asymptotic central limit theorem, where the convergence rate in Wasserstein distance explicitly reflects the…

We consider the behavior of spatial point processes when subjected to a class of linear transformations indexed by a variable T. It was shown in Ellis [Adv. in Appl. Probab. 18 (1986) 646-659] that, under mild assumptions, the transformed…