Related papers: Statistical convergence of order $\alpha$ in proba…
We study some new strongly almost lacunary statistical $A$-convergent sequence space of order $\alpha$ defined by a Musielak-Orlicz function. We also give some inclusion relations between the newly introduced class of sequences with the…
We study the stochastic convergence of the Ces\`{a}ro mean of a sequence of random variables. These arise naturally in statistical problems that have a sequential component, where the sequence of random variables is typically derived from a…
A sequence $(x_n)$ in a lattice-normed space $(X,p,E)$ is statistical $p$-convergent to $x\in X$ if there exists a statistical $p$-decreasing sequence $q\stpd 0$ with an index set $K$ such that $\delta(K)=1$ and $p(x_{n_k}-x)\leq q_{n_k}$…
In this research article, we have primarily focused on the circumstantial investigation of deferred statistical convergence of sequences and investigated some fundamental results compatible with the structure of a probabilistic normed…
In this paper we introduce the notions of statistical convergence and statistical Cauchyness of sequences in a metric-like space. We study some basic properties of these notions
This survey concerns probabilistic models motivated by cooperative sequential adsorption (CSA) models. CSA models are widely used in physics and chemistry for modelling adsorption processes in which adsorption rates depend on the spatial…
In this note, we study convergence rates in the law of large numbers for independent and identically distributed random variables under sublinear expectations. We obtain a strong $L^p$-convergence version and a strongly quasi sure…
The purpose of this paper is twofold. First, the definition of new statistical convergence with Fibonacci sequence is given and some fundamental properties of statistical convergence are examined. Second, approximation theory worked as a…
In this paper, we study the summability properties of double sequences of real constants which map sequences of random variables to sequences of random variables that are defined on the same probability sample space. We show that a regular…
We introduce and study deferred N\"{o}rlund statistical convergence in probability, mean of order $r,$ distribution, and study the interrelation among them. Based upon the proposed method to illustrate the findings, we present new Korovkin…
In this article the idea of random variables over the set theoretic universe is investigated. We explore what it can mean for a random set to have a specific probability of belonging to an antecedently given class of sets.
We describe five types of results concerning information and concentration of discrete random variables, and relationships between them, motivated by their counterparts in the continuous case. The results we consider are information…
A lacunary sequence is an increasing integer sequence $\theta=(k_r)$ such that $k_r-k_{r-1}\rightarrow \infty$ as $r\rightarrow \infty.$ In this article we introduce arithmetic statistically convergent sequence space $ASC$ and lacunary…
Convolutions of independent random variables often arise in a natural way in many applied problems. In this article, we compare convolutions of two sets of gamma (negative binomial) random variables in the convolution order and the usual…
We give a model-theoretic account for several results regarding sequences of random variables appearing in Berkes & Rosenthal \cite{Berkes-Rosenthal:AlmostExchangeableSequences}. In order to do this, {itemize} We study and compare three…
We investigate quantitative implications of the notion of log-concavity through a probabilistic interpretation. In particular, we derive concentration inequalities, moment and entropy bounds for random variables satisfying a precise degree…
The usual stochastic order and the likelihood ratio order between probability distributions on the real line are reviewed in full generality. In addition, for the distribution of a random pair $(X,Y)$, it is shown that the conditional…
In the classical probability in continuous random variables there is no distinguishing between the probability involving strict inequality and non strict inequality. Moreover a probability involves equality collapse to zero without…
Let $X_1, X_2,\ldots, X_n$ (resp. $Y_1, Y_2,\ldots, Y_n$) be independent random variables such that $X_i$ (resp. $Y_i$) follows generalized exponential distribution with shape parameter $\theta_i$ and scale parameter $\lambda_i$ (resp.…
In the present paper we will give some new notions, such as {\Delta}-convergence and {\Delta}-Cauchy, by using the {\Delta}-density and investigate their relations. It is important to say that, the results presented in this work generalize…