Related papers: On Abel statistical convergence
In this paper, using the concept of natural density, we have introduced the ideas of statistical and rough statistical convergence in an $S$-metric space. We have investigated some of their basic properties. We have defined statistical…
In the present paper, we introduce a new concept of convexity which is generated by a family of endomorphisms of an Abelian group. In Abelian groups equipped with a translation invariant metric, we define the boundedness, the norm, the…
We show that the patterns in the Abelian sandpile are stable. The proof combines the structure theory for the patterns with the regularity machinery for non-divergence form elliptic equations. The stability results allows one to improve…
After a short review of the historical milestones on normal numbers, we introduce the Borel numbers as the reals admitting a probability function on their different bases representations. In this setting, we provide two probabilistic…
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
The notion of representative statistical ensembles, correctly representing statistical systems, is strictly formulated. This notion allows for a proper description of statistical systems, avoiding inconsistencies in theory. As an…
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like…
We propose a novel approach to parameter estimation for simulator-based statistical models with intractable likelihood. Our proposed method involves recursive application of kernel ABC and kernel herding to the same observed data. We…
Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…
A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell: G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant…
By a classical result of Gauss and Kuzmin, the continued fraction expansion of a ``random'' real number contains each digit $a\in\mathbb{N}$ with asymptotic frequency $\log_2(1+1/(a(a+2)))$. We generalize this result in two directions:…
Let $(\Omega,{\cal F},P)$ be a probability space and $L^{0}({\cal F},R)$ the algebra of equivalence classes of real-valued random variables on $(\Omega,{\cal F},P)$. When $L^{0}({\cal F},R)$ is endowed with the topology of convergence in…
We study the convergence of probability measures in terms of moments by applying operators to their Bessel generating functions. We consider a general setting of applying operators such as the Dunkl operator to formal power series that are…
We investigate the properties of a sequential Monte Carlo method where the particle weight that appears in the algorithm is estimated by a positive, unbiased estimator. We present broadly-applicable convergence results, including a central…
Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…
Probability distributions supported on the simplex enjoy a wide range of applications across statistics and machine learning. Recently, a novel family of such distributions has been discovered: the continuous categorical. This family enjoys…
With the emergence of high-throughput technologies, it is possible to measure large amounts of data relatively at low cost. Such situations arise in many fields from sciences to humanities, and variable selection may be of great help to…
Summation of a large class of the functional series, which terms contain factorials, is considered. We first investigated finite partial sums for integer arguments. These sums have the same values in real and all p-adic cases. The…
A real number \alpha is called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to \alpha. The randomness of a recursively enumerable real \alpha can be characterized in various…