Related papers: Deviation inequalities for sums of weakly dependen…

We establish discrete Ingham type and Haraux type inequalities for exponential sums satisfying a weakened gap condition. They enable us to obtain discrete simultaneous observability theorems for systems of vibrating strings or beams.

We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…

Modeling univariate block maxima by the generalized extreme value distribution constitutes one of the most widely applied approaches in extreme value statistics. It has recently been found that, for an underlying stationary time series,…

In this paper, we obtain precise rates of convergence in the strong invariance principle for stationary sequences of real-valued random variables satisfying weak dependence conditions including strong mixing in the sense of Rosenblatt…

In this paper, we are concerned with obtaining distribution-free concentration inequalities for mixture of independent Bernoulli variables that incorporate a notion of variance. Missing mass is the total probability mass associated to the…

This paper is concerned with relationships of weakly mixing, topologically weakly mixing, and sensitivity for non-autonomous discrete systems. It is shown that weakly mixing implies topologically weakly mixing and sensitivity for measurable…

We derive a new class of time-dependent Bell inequalities in Wigner form under the assumption of locality in the framework of Kolmogorov's probability theory. We consider violation of the obtained inequalities for three cases: spin…

This work focuses on moderate deviations for two-time scale systems with mixed fractional Brownian motion. Our proof uses the weak convergence method which is based on the variational representation formula for mixed fractional Brownian…

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of…

This paper is concerned with the weak solvability of fully nonlinear parabolic variational inequalities with time dependent convex constraints. As possible approaches to such problems, there are for instance the time-discretization method…

Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…

We study complete convergence and closely related Hsu-Robbins-Erd\H{o}s-Spitzer-Baum-Katz series for sums whose terms are elements of linear autoregression sequences. We obtain criterions for convergence of this series expressed in moment…

We study simple models of intermittency, involving switching between two states, within the dynamical large-deviation formalism. Singularities appear in the formalism when switching is cooperative, or when its basic timescale diverges. In…

We provide an inequality which is a useful tool in studying both large deviation results and limit theorems for sums of random fields with "negligible" small values. In particular, the inequality covers cases of stable limits for random…

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely…

We establish concentration inequalities for random dynamical systems (RDSs), assuming that the observables of interest are separately Lipschitz. Under a weak average contraction condition, we obtain deviation bounds for several random…

We prove a new Bernstein-type inequality for the log-likelihood function of Bernoulli variables. In contrast to classical Bernstein's inequality and Hoeffding's inequality when applied to the log-likelihood, the new bound is independent of…

A method for detecting possible non-deterministic dynamics underlying a time series is introduced. Non-deterministic dynamics may arise due to the failure of the Lipschitz condition in the equations of motion. At a singular point, the phase…

We consider a system of seminlinear parabolic variational inequalities with time-dependent convex obstacles. We prove the existence and uniqueness of its solution. We also provide a stochastic representation of the solution and show that it…

In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.