Related papers: Summability of Sequence of Random Variables

We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…

Summability methods for ultraholomorphic classes in sectors, defined in terms of a strongly regular sequence $\mathbb{M}=(M_p)_{p\in\mathbb{N}_0}$, have been put forward by A. Lastra, S. Malek and the second author (Summability in general…

We prove that the distribution of the product of two correlated normal random variables with arbitrary means and arbitrary variances is infinitely divisible. We also obtain exact formulas for the probability density function of the sum of…

I present here some results on the statistical behaviour of large random matrices in an ensemble where the probability distribution is not a function of the eigenvalues only. The perturbative expansion can be cast in a closed form and the…

In the present paper we propose generalizations of the regularity and counting lemmas for multidimensional matrices under a finite alphabet. Firstly, we prove a variant of a multidimensional regularity lemma with the help of a translation…

This note examines the infinite divisibility of density-based transformations of normal random variables. We characterize a class of density-based transformations of normal variables which produces non-infinitely divisible distributions. We…

Various methods of summation for divergent series of real numbers have been generalized to analogous results for sums of iid random variables. The natural extension of results corresponding to Ces\`aro summation amounts to proving almost…

We give an extension of Sister Celine's method of proving hypergeometric sum identities that allows it to handle a larger variety of input summands. We then apply this to several problems. Some give new results, and some reprove already…

The paper is the second of our series of notes aimed to bring back in circulation some bright ideas of early modern set theory, mainly due to Harrington and Sami, which have never been adequately presented in set theoretic publications. We…

We study the gaps between consecutive singular values of random rectangular matrices. Specifically, if $M$ is an $n \times p$ random matrix with independent and identically distributed entries and $\Sigma$ is a $n \times n$ deterministic…

We study the question, ``For which reals $x$ does there exist a measure $\mu$ such that $x$ is random relative to $\mu$?'' We show that for every nonrecursive $x$, there is a measure which makes $x$ random without concentrating on $x$. We…

In this paper we have characterized the space of summability kernels for the case p=1 and p=2. For other values of p we give a necessary condition for a function $\Lambda$ to be a summability kernel. For the case p=1, we have studied the…

This paper examines the foundational concept of random variables in probability theory and statistical inference, demonstrating that their mathematical definition requires no reference to randomization or hypothetical repeated sampling. We…

We further investigate the uniform regularity property of collections of sets via primal and dual characterizing constants. These constants play an important role in determining convergence rates of projection algorithms for solving…

To develop an approach to utilizing continuous statistical information within the Dempster- Shafer framework, we combine methods proposed by Strat and by Shafero We first derive continuous possibility and mass functions from…

We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…

This paper considers how to measure the magnitude of the sum of independent random variables in several ways. We give a formula for the tail distribution for sequences that satisfy the so called Levy property. We then give a connection…

The subject of this paper is regularity-preserving aggregation of regular norms on finite-dimensional linear spaces. Regular norms were introduced in [5] and are closely related to ``type 2'' spaces [9, Chapter 9] playing important role in…

We introduce the problem of variable-length source resolvability, where a given target probability distribution is approximated by encoding a variable-length uniform random number, and the asymptotically minimum average length rate of the…

We present a convex approach to probabilistic segmentation and modeling of time series data. Our approach builds upon recent advances in multivariate total variation regularization, and seeks to learn a separate set of parameters for the…