Related papers: Malliavin-Stein method for multi-dimensional U-sta…
Initiated around the year 2007, the Malliavin-Stein approach to probabilistic approximations combines Stein's method with infinite-dimensional integration by parts formulae based on the use of Malliavin-type operators. In the last decade,…
In this paper we extend the refined second-order Poincar\'e inequality for Poisson functionals from a one-dimensional to a multi-dimensional setting. Its proof is based on a multivariate version of the Malliavin-Stein method for normal…
We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and…
We apply the Stein-Chen method to problems from extreme value theory. On the one hand, the Stein-Chen method for Poisson approximation allows us to obtain bounds on the Kolmogorov distance between the law of the maximum of i.i.d. random…
We establish inequalities for assessing the distance between the distribution of errors of partially observed high-frequency statistics of multidimensional L\'evy processes and that of a mixed Gaussian random variable. Furthermore, we…
We derive Gaussian approximation bounds for $k$-Potential Nearest Neighbor ($k$-PNN) based random forest predictions based on a set of training points given by a Poisson process under fairly mild regularity assumptions on the data…
The main purpose of the paper is to investigate the possibility of applying Chen-Stein approach to estimate the $\chi^2$ distance between Poisson distribution and a sum of independent indicators. Earlier results concerning $\chi^2$ distance…
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…
Given a random variable $F$ regular enough in the sense of the Malliavin calculus, we are able to measure the distance between its law and almost any continuous probability law on the real line. The bounds are given in terms of the…
Using Stein's method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence…
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…
Based on Stein's method, we derive upper bounds for Poisson process approximation in the $L_1$-Wasserstein metric $d_2^{(p)}$, which is based on a slightly adapted $L_p$-Wasserstein metric between point measures. For the case $p=1$, this…
An analogue of Talagrand's convex distance for binomial and Poisson point processes is defined. A corresponding large deviation inequality is proved.
We give estimates of the distance between the densities of the laws of two functionals $F$ and $G$ on the Wiener space in terms of the Malliavin-Sobolev norm of $F-G.$ We actually consider a more general framework which allows one to treat…
Lower bounds for variances are often needed to derive central limit theorems. In this paper, we establish a lower bound for the variance of Poisson functionals that uses the difference operator of Malliavin calculus. Poisson functionals,…
In recent years, infinite-dimensional methods have been introduced for the Gaussian channels estimation. The aim of this paper is to study the application of similar methods to Poisson channels. In particular we compute the Bayesian…
This article compares the distributions of integer-valued random variables and Poisson random variables. It considers the total variation and the Wasserstein distance and provides, in particular, explicit bounds on the pointwise difference…
We consider a real-valued diffusion process with a linear jump term driven by a Poisson point process and we assume that the jump amplitudes have a centered density with finite moments. We show upper and lower estimates for the density of…
We develop a functional Stein-Malliavin method in a non-diffusive Poissonian setting, thus obtaining a) quantitative central limit theorems for approximation of arbitrary non-degenerate Gaussian random elements taking values in a separable…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…