相关论文: Gaussian Approximation and Moderate Deviations of …

Consider a homogeneous Poisson process in $\mathbb{R}^d$, $d \ge 1$. Let $R_1 < R_2 < \dots$ be the distances of the points from the origin, and let $S = R_1^{-\gamma} + R_2^{-\gamma} + \dots$, where $\gamma > d$ is a parameter. Let…

We prove a bound for the Wasserstein distance between vectors of smooth complex random variables and complex Gaussians in the framework of complex Markov diffusion generators. For the special case of chaotic eigenfunctions, this bound can…

In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared…

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on…

We derive first-order (in the stepsize) bounds on the bias in Wasserstein distances of the invariant measure of stochastic gradient kinetic Langevin dynamics with minimal assumptions on the stochastic gradient noise. These bounds sharpen…

Consider an unlimited homogeneous medium disturbed by points generated via Poisson process. The neighborhood of a point plays an important role in spatial statistics problems. Here, we obtain analytically the distance statistics to $k$th…

Given a reference random variable, we study the solution of its Stein equation and obtain universal bounds on its first and second derivatives. We then extend the analysis of Nourdin and Peccati by bounding the Fortet-Mourier and…

We prove limit theorems for functionals of a Poisson point process using the Malliavin calculus on the Poisson space. The target distribution is conditionally either a Gaussian vector or a Poisson random variable. The convergence is stable…

In this article, we obtain, for the total variance distance, the error bounds between Poisson and convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several…

We derive two estimates for the deviation of the $N$-particle, hard-spheres Kac process from the corresponding Boltzmann equation, measured in expected Wasserstein distance. Particular care is paid to the long-time properties of our…

This paper derives lower bounds for the mean square errors of parameter estimators in the case of Poisson distributed data subjected to multiple abrupt changes. Since both change locations (discrete parameters) and parameters of the Poisson…

The Vlasov-Poisson system is widely used in plasma physics and other related fields. In this paper, we study the Vlasov-Poisson system with initial uncertainty in the quasineutral regime. First, we prove the uniform convergence in the…

We obtain quenched hitting distributions to be compound Poissonian for a certain class of random dynamical systems. The theory is general and designed to accommodate non-uniformly expanding behavior and targets that do not overlap much with…

Let $Y=X_1+\cdots+X_N$ be a sum of a random number of exchangeable random variables, where the random variable $N$ is independent of the $X_j$, and the $X_j$ are from the generalized multinomial model introduced by Tallis (1962). This…

We study the problem of approximately recovering a probability distribution given noisy measurements of its Chebyshev polynomial moments. This problem arises broadly across algorithms, statistics, and machine learning. By leveraging a…

We derive upper bounds on the Wasserstein distance ($W_1$), with respect to $\sup$-norm, between any continuous $\mathbb{R}^d$ valued random field indexed by the $n$-sphere and the Gaussian, based on Stein's method. We develop a novel…

This paper develops the large deviations theory for the point process associated with the Euclidean volume of $k$-nearest neighbor balls centered around the points of a homogeneous Poisson or a binomial point processes in the unit cube. Two…

Poisson approximation using Stein's method has been extensively studied in the literature. The main focus has been on bounding the total variation distance. This paper is a first attempt on moderate deviations in Poisson approximation for…

We introduce a general framework that constructs estimators with reduced variance for random walk Metropolis and Metropolis-adjusted Langevin algorithms. The resulting estimators require negligible computational cost and are derived in a…

We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…