Refined convergence for the Boolean model

A Berry Esseen type limit theorem for Boolean convolution

We give estimates on the rate of convergence in the Boolean central limit theorem for the Lévy distance. In the case of measures with bounded support we obtain a sharp estimate by giving a qualitative description of this convergence.

On a Berry-Esseen type limit theorem for Boolean convolution

We obtain a sharp estimate of the speed of convergence in the Boolean central limit theorem for measures of finite sixth moment. The main tool is a quantitative version of the Stieltjes-Perron inversion formula.

在von Mises条件下向布尔极值分布收敛的速度研究

On the rate of convergence to the Boolean extreme value distribution under the von Mises condition

研究在von Mises条件下，布尔独立同分布正算子归一化谱极大值收敛到布尔极值分布的速度，探讨其收敛速率及极限分布特性。

Refined properties for the Mellin transform, with applications to convergence of families obtained by biasing or by the stationary excess operator

We first provide some properties of the Mellin transform of nonnegative random variables, such that monotonicity, injectivity and effect of size biasing. Convergence of Mellin transforms is also entirely formalized through convergence in distribution and uniform integrability. As an application, we study a problem raised by Harkness and Shantaram (1969) who obtained, under sufficient conditions, a limit theorem for sequences of nonnegative random variables build with the iterated stationary excess operator. We reformulate this problem through the concept of multiply monotone functions and thro…

Asymptotics of the visibility function in the Boolean model

The aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle in a Boolean model. We proceed in two or more dimensions using coverage techniques. Moreover, convergence results involving a type I extreme value distribution are shown in the two particular cases of small obstacles or a large obstacle-free region.

Refined basic couplings and Wasserstein-type distances for SDEs with Lévy noises

We establish the exponential convergence with respect to the $L^1$-Wasserstein distance and the total variation for the semigroup corresponding to the stochastic differential equation (SDE) $$d X_t=d Z_t+b(X_t)\,d t,$$ where $(Z_t)_{t\ge0}$ is a pure jump Lévy process whose Lévy measure $ν$ fulfills $$ \inf_{x\in \R^d, |x|\le κ_0} [ν\wedge (δ_x \ast ν)]( \R^d)>0$$ for some constant $κ_0>0$, and the drift term $b$ satisfies that for any $x,y\in \R^d$, $$\langle b(x)-b(y),x-y\rangle\le \begin{cases} Φ_1(|x-y|)|x-y|,& |x-y|\le l_0; -K_2|x-y|^2,& |x-y|> l_0 \end{cases}$$ with some positive constan…