Related papers: On the accuracy in a combinatorial central limit t…

We consider Berry's random planar wave model (1977), and prove spatial functional limit theorems - in the high-energy limit - for discretized and truncated versions of the random field obtained by restricting its nodal length to rectangular…

Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the…

This is the second component of a two-part paper dealing with a unification of characteristic mode decomposition. This second part addresses modal tracking and losses and presents several numerical examples for both surface- and…

This paper derives exponential tail bounds and polynomial moment inequalities for the spectral norm deviation of a random matrix from its mean value. The argument depends on a matrix extension of Stein's method of exchangeable pairs for…

Let $Z$ be a Boolean model based on a stationary Poisson process $\eta$ of compact, convex particles in Euclidean space ${\mathbb{R}}^d$. Let $W$ denote a compact, convex observation window. For a large class of functionals $\psi$, formulas…

We obtain a Bernstein type Gaussian concentration inequality for martingales. Our inequality improves the Azuma-Hoeffding inequality for moderate deviations $x$. Following the work of McDiarmid (1989), Talagrand (1996) and Boucheron, Lugosi…

Motivated by the goal of improving the efficiency of small sample design, we propose a novel Bayesian stochastic approximation method to estimate the root of a regression function. The method features adaptive local modelling and…

Let $(g_{n})_{n\geq 1}$ be a sequence of independent and identically distributed positive random $d\times d$ matrices and consider the matrix product $G_n: = g_n \ldots g_1$. Under suitable conditions, we establish the Berry-Esseen bounds…

Despite its generality and powerful convergence properties, Milstein's method for functionals of spatially bounded stochastic differential equations is widely regarded as difficult to implement. This has likely prevented it from being…

As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using It\^o's formula and on a new…

A new inequality between some functional of probability distribution functions is given. The inequality is based on strict convexity of a function used in functional definition. Equality sign in the inequality gives a characteristic…

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

In this paper we present a fully deterministic method for the numerical solution to the Boltzmann equation of rarefied gas dynamics in a bounded domain for multi-scale problems. Periodic, specular reflection and diffusive boundary…

In this paper we present a method of characteristic sets for inversive difference polynomials and apply it to the analysis of systems of quasi-linear algebraic difference equations. We describe characteristic sets and compute difference…

Bayesian inference provides a principled way of estimating the parameters of a stochastic process that is observed discretely in time. The overdamped Brownian motion of a particle confined in an optical trap is generally modelled by the…

Bernstein polynomial approximation to a continuous function has a slower rate of convergence as compared to other approximation methods. "The fact seems to have precluded any numerical application of Bernstein polynomials from having been…

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 obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…

We give some rates of convergence in the distances of Kolmogorov and Wasserstein for standardized martingales with differences having finite variances. For the Kolmogorov distances, we present some exact Berry-Esseen bounds for martingales,…

We consider solutions of stochastic differential equations which diverge to infinity as the time parameter goes to infinity. If the coefficients converge as the spacial variable goes to infinity, then the solutions will get close to some…