Related papers: Nonconventional moderate deviations theorems and e…
In this paper we obtain the limit distribution for partial sums with a random number of terms following a class of mixed Poisson distributions. The resulting weak limit is a mixing between a normal distribution and an exponential family,…
Large deviation inequalities for ergodic sums is an important subject since the seminal contribution of Bernstein for independent random variables with finite variances, followed by the Chernoff method and the Hoefding result for…
This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…
Edgeworth-type expansions for convolutions of probability densities and powers of the characteristic functions with non-uniform error terms are established for i.i.d. random variables with finite (fractional) moments of order $s \geq 2$,…
In this paper we obtain a Bernstein type inequality for the sum of self-adjoint centered and geometrically absolutely regular random matrices with bounded largest eigenvalue. This inequality can be viewed as an extension to the matrix…
In this article, we obtain explicit bounds on the uniform distance between the cumulative distribution function of a standardized sum $S_n$ of $n$ independent centered random variables with moments of order four and its first-order…
We derive both Azuma-Hoeffding and Burkholder-type inequalities for partial sums over a rectangular grid of dimension $d$ of a random field satisfying a weak dependency assumption of projective type: the difference between the expectation…
Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…
This note is concerned with concentration inequalities for extrema of stationary Gaussian processes. It provides non-asymptotic tail inequalities which fully reflect the fluctuation rate, and as such improve upon standard Gaussian…
Our purpose is to prove central limit theorem for countable nonhomogeneous Markov chain under the condition of uniform convergence of transition probability matrices for countable nonhomogeneous Markov chain in Ces\`aro sense. Furthermore,…
A moderate deviation principle for functionals, with at most quadratic growth, of moving average processes is established. The main assumptions on the moving average process are a Logarithmic Sobolev inequality for the driving random…
We modify the classical Bernstein's inequality for the sums of independent centered random variables (r.v.) in the terms of relative tails or moments. We built also some examples in order to show the exactness of offered results.
Moderate deviations for random complex zeroes are deduced from a new theorem on moderate deviations for random fields.
We prove a Bennett-type concentration bound for suprema of empirical processes based on sampling without replacement and a corresponding bound in the case of an arbitrary Hoeffding statistics. We improve on the previous results of such…
We consider a class of tempered subordinators, namely a class of subordinators with one-dimensional marginal tempered distributions which belong to a family studied in [3]. The main contribution in this paper is a non-central moderate…
This work is devoted to the study of the nonlinear second-order neutral difference equations with quasi-differences of the form $$ \Delta \left( r_{n} \Delta \left( x_{n}+q_{n}x_{n-\tau}\right)\right)= a_{n}f(x_{n-\sigma})+b_n%, \ n\geq n_0…
We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…
Let $X_1,...,X_n$ be $n$ independent unbounded real random variables which have common, roughly speaking, light-tailed type distribution. Denote by $S_1^n$ their sum and by $\pi^{a_n}$ the tilted density of $X_1$, where $a_n…
We formulate uncertainty relations for arbitrary $N$ observables. Two uncertainty inequalities are presented in terms of the sum of variances and standard deviations, respectively. The lower bounds of the corresponding sum uncertainty…
An important tool for statistical research are moment inequalities for sums of independent random vectors. Nemirovski and coworkers (1983, 2000) derived one particular type of such inequalities: For certain Banach spaces $(\B,\|\cdot\|)$…