Related papers: Normal approximation for associated point processe…
We generalize the Poisson limit theorem to binary functions of random objects whose law is invariant under the action of an amenable group. Examples include stationary random fields, exchangeable sequences, and exchangeable graphs. A…
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays an important role in the study…
We propose two families of tests for the classical goodness-of-fit problem to univariate normality. The new procedures are based on $L^2$-distances of the empirical zero-bias transformation to the normal distribution or the empirical…
We use Stein's method to obtain a bound on the distance between scaled $p$-dimensional random walks and a $p$-dimensional (correlated) Brownian Motion. We consider dependence schemes including those in which the summands in scaled sums are…
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
In this article, we discuss the basic ideas of a general procedure to adapt the Stein-Chen method to bound the distance between conditional distributions. From an integration-by-parts formula (IBPF), we derive a Stein operator whose…
We establish uniform pointwise estimates for the densities of a family of $\alpha$-stable processes with respect to the index $\alpha \in [\alpha_0,2]$ for some $\alpha_0>0$. In addition, we estimate the difference between the heat kernels…
In this article, we present a method for approximating affine processes on the cone of positive Hilbert-Schmidt operators using matrix-valued affine processes. By leveraging results from the theory on affine processes with values in the…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
We introduce the affine ensemble, a class of determinantal point processes (DPP) in the half-plane C^+ associated with the ax+b (affine) group, depending on an admissible Hardy function {\psi}. We obtain the asymptotic behavior of the…
Directional data require specialized probability models because of the non-Euclidean and periodic nature of their domain. When a directional variable is observed jointly with linear variables, modeling their dependence adds an additional…
We provide a Poisson approximation result for dependent thinnings of Gibbs point processes as well as qualitative and quantitative central limit theorems for geometric functionals of Gibbs point processes in increasing observation windows.…
Let $\Delta\subsetneq\V$ be a proper subset of the vertices $\V$ of the defining graph of an irreducible and aperiodic shift of finite type $(\Sigma_{A}^{+},\S)$. Let $\Sigma_{\Delta}$ be the subshift of allowable paths in the graph of…
In this paper a drift-randomized Milstein method is introduced for the numerical solution of non-autonomous stochastic differential equations with non-differentiable drift coefficient functions. Compared to standard Milstein-type methods we…
We provide an overview of some recent techniques involving the Malliavin calculus of variations and the so-called ``Stein's method'' for the Gaussian approximations of probability distributions. Special attention is devoted to establishing…
In this paper we give a historical account of the development of Poisson approximation using Stein's method and present some of the main results. We give two recent applications, one on maximal arithmetic progressions and the other on…
Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we…
We derive explicit central moment inequalities for random variables that admit a Stein coupling, such as exchangeable pairs, size--bias couplings or local dependence, among others. The bounds are in terms of moments (not necessarily…
We define a new type of self-similarity for one-parameter families of stochastic processes, which applies to a number of important families of processes that are not self-similar in the conventional sense. This includes a new class of…
We establish a quantitative normal approximation result for sums of random variables with multilevel local dependencies. As a corollary, we obtain a quantitative normal approximation result for linear functionals of random fields which may…