Related papers: Stein approximation for multidimensional Poisson r…
Several classical results on boundary crossing probabilities of Brownian motion and random walks are extended to asymptotically Gaussian random fields, which include sums of i.i.d. random variables with multidimensional indices,…
In a recent paper, Gaunt 2020 extended Stein's method to limit distributions that can be represented as a function $g:\mathbb{R}^d\rightarrow\mathbb{R}$ of a centered multivariate normal random vector $\Sigma^{1/2}\mathbf{Z}$ with…
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…
In this paper, following Nourdin-Peccati's methodology, we combine the Malliavin calculus and Stein's method to provide general bounds on the Wasserstein distance between functionals of a compound Hawkes process and a given Gaussian…
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…
This paper derives normal approximation results for subgraph counts written as multiparameter stochastic integrals in a random-connection model based on a Poisson point process. By combinatorial arguments we express the cumulants of general…
In this paper, we apply the Stein's method in the context of point processes, namely when the target measure is the distribution of a finite Poisson point process. We show that the so-called Kantorovich-Rubinstein distance between such a…
"Quantum trajectories" are solutions of stochastic differential equations of non-usual type. Such equations are called "Belavkin" or "Stochastic Schr\"odinger Equations" and describe random phenomena in continuous measurement theory of Open…
This article presents a coupling approach for the approximation of iterated stochastic integrals of length three. The generation of such integrals is the central problem of higher-order pathwise approximations for SDEs, which still lacks a…
In this paper, we study the diffusion approximation for singularly perturbed stochastic reaction-diffusion equation with a fast oscillating term. The asymptotic limit for the original system is obtained, where an extra Gaussian term…
In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…
General Berry-Esseen bounds are developed for the exponential distribution using Stein's method. As an application, a sharp error term is obtained for Hora's result that the spectrum of the Bernoulli-Laplace Markov chain has an exponential…
The (conditional or unconditional) distribution of the continuous scan statistic in a one-dimensional Poisson process may be approximated by that of a discrete analogue via time discretization (to be referred to as the discrete…
Edgeworth expansions for random walks on covering graphs with groups of polynomial volume growths are obtained under a few natural assumptions. The coefficients appearing in this expansion depends on not only geometric features of the…
We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…
Stein's method allows to prove distributional convergence of a sequence of random variables and to quantify it with respect to a given metric such as Kolmogorov's (a Berry-Ess\'een type theorem). Mod-* convergence quantifies the convergence…
Stein discrepancies (SDs) monitor convergence and non-convergence in approximate inference when exact integration and sampling are intractable. However, the computation of a Stein discrepancy can be prohibitive if the Stein operator - often…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
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…
Let F ($\nu$) be the centered Gamma law with parameter $\nu$ > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to…