Related papers: Random differences in Szemer\'edi's theorem and re…
A random coefficient autoregressive process is deeply investigated in which the coefficients are correlated. First we look at the existence of a strictly stationary causal solution, we give the second-order stationarity conditions and the…
We prove a version of a general transfer theorem for random sequences with independent random indexes in the double array limit setting under relaxed conditions. We also prove its partial inverse providing the necessary and sufficient…
We extend some sharp inequalities for martingale-differences to general multiplicative systems of random variables. The key ingredient in the proofs is a technique reducing the general case to the case of Rademacher random variables without…
This paper describes a methodology for detecting anomalies from sequentially observed and potentially noisy data. The proposed approach consists of two main elements: (1) {\em filtering}, or assigning a belief or likelihood to each…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Some tools and ideas are interchanged between random matrix theory and multivariate statistics. In the context of the random matrix theory, classes of spherical and generalised Wishart random matrix ensemble, containing as particular cases…
A major theme in arithmetic combinatorics is proving multiple recurrence results on semigroups (such as Szemer\'edi's theorem) and this can often be done using methods of ergodic Ramsey theory. What usually lies at the heart of such proofs…
We study a well-known problem concerning a random variable $Z$ uniformly distributed between two independent random variables. A new extension has been introduced for this problem and fairly large classes of randomly weighted average…
An improved estimate is given for $|\theta(x) -x|$, where $\theta(x) = \sum_{p\leq x} \log p$. Three applications are given: the first to arithmetic progressions that have points in common, the second to primes in short intervals, and the…
Let $\{X_{i}, i\in J\}$ be a family of locally dependent non-negative integer-valued random variables with finite expectations and variances. We consider the sum $W=\sum_{i\in J}X_i$ and use Stein's method to establish general upper error…
We want to select the best systems out of a given set of systems (or rank them) with respect to their expected performance. The systems allow random observations only and we assume that the joint observation of the systems has a…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
Deep learning-based methods have achieved a breakthrough in image anomaly detection, but their complexity introduces a considerable challenge to understanding why an instance is predicted to be anomalous. We introduce a novel explanation…
We apply Lindeberg's method, invented to prove a central limit theorem, to analyze the moderate deviations around such a central limit theorem. In particular, we will show moderate deviation principles for martingales as well as for random…
This paper investigates the use of different transformations for improving the randomness of sequences. In particular, convolutional codes are used for increasing the size of a given sequence and then a random mapping function is used for…
The study of several naturally arising "nearest neighbours" random walks benefits from the study of the associated orthogonal polynomials and their orthogonality measure. I consider extensions of this approach to a larger class of random…
Ordinary Differential Equations are generally too complex to be solved analytically. Approximations thereof can be obtained by general purpose numerical methods. However, even though accurate schemes have been developed, they remain…
Rerandomization is a strategy of increasing efficiency as compared to complete randomization. The idea with rerandomization is that of removing allocations with imbalance in the observed covariates and then randomizing within the set of…
By means of a variational approach we find new series representations both for well known mathematical constants, such as $\pi$ and the Catalan constant, and for mathematical functions, such as the Riemann zeta function. The series that we…
Convergence results for averages of independent replications of counting processes are established in a $p$-variation setting and under certain assumptions. Such convergence results can be combined with functional differentiability results…