Related papers: Deviation and moment inequalities for Banach-value…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
This paper deals with U-statistics of Poisson processes and multiple Wiener-It\^o integrals on the Poisson space. Via sharp bounds on the cumulants for both classes of random variables, moderate deviation principles, concentration…
We develop a theory of Malliavin calculus for Banach space valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener-Ito isometry to Banach spaces. In the white noise case we obtain two…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
We consider real-valued branching random walks and prove a large deviation result for the position of the rightmost particle. The position of the rightmost particle is the maximum of a collection of a random number of dependent random…
We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus propose a robust test based on the Wilcoxon two-sample test statistic.…
We quantify the elementary Borel-Cantelli Lemma by higher moments of the overlap count statistic in terms of the weighted summability of the probabilities. Applications include mean deviation frequencies in the Strong Law and the Law of the…
A condition on a Banach function space $X$ is given under which the Coifman-Fefferman and Fefferman-Stein inequalities on $X$ are equivalent.
We develop Gaussian approximations for high-dimensional vectors formed by second-order $U$- and $V$-statistics whose kernels depend on sample size under independent but not identically distributed (i.n.i.d.) sampling. Our results hold…
In this article, we develop a framework to study the large deviation principle for matrix models and their quantized versions, by tilting the measures using the limits of spherical integrals obtained in [46,47]. As examples, we obtain 1. a…
We give a criterion to determine the large deviation rate functions for abstract dynamical systems on towers. As an application of this criterion we show the level 2 large deviation principle for some class of smooth interval maps with…
We study the convergence of statistical estimators used in the estimation of large deviation functions describing the fluctuations of equilibrium, nonequilibrium, and manmade stochastic systems. We give conditions for the convergence of…
We provide a limit theory for a general class of kernel smoothed U-statistics that may be used for specification testing in time series regression with nonstationary data. The test framework allows for linear and nonlinear models with…
In this paper, several differentiability criteria for real functions of multiple variables in n-dimensional Euclidean space are considered. Simple and easy-to-use Cauchy-like criterion is formulated and proven. Relaxed sufficient conditions…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
In this paper we study set convergence aspects for Banach spaces of vector-valued measures with divergences (represented by measures or by functions) and applications. We consider a form of normal trace characterization to establish…
In this paper we investigate four concepts of exponential stability for difference equations in Banach spaces. Characterizations of these concepts are given. They can be considered as variants for the discrete-time case of the classical…
We consider in this paper the problem of sampling a high-dimensional probability distribution $\pi$ having a density with respect to the Lebesgue measure on $\mathbb{R}^d$, known up to a normalization constant $x \mapsto \pi(x)=…
Necessary and sufficient criteria for metric subregularity (or calmness) of set-valued mappings between general metric or Banach spaces are treated in the framework of the theory of error bounds for a special family of extended real-valued…
In this article we present a Bernstein inequality for sums of random variables which are defined on a graphical network whose nodes grow at an exponential rate. The inequality can be used to derive concentration inequalities in…