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Convergence
Convergence is an important aspect of the computation of probabilities. It can be defined in many ways, each type of convergence having its own...
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Digital Convergence
High-Performance Computing has recently been challenged by the advent of Artificial Intelligence. Artificial Intelligence has become rather popular...
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Convergence in Distribution
The next fundamental notion of convergence after almost-sure convergence is convergence in distribution, and the main result there is the central...
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Convergence and Continuity
The idea of a sequence converging to a limit is defined rigorously in a general metric space. Examples are taken from real analysis, and it is shown...
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Modes of Convergence
To estimate an unknown parameter, we can draw some independent samples and obtain an estimator from the samples. It is natural to ask whether the...
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Convergence of Estimators
Chapter 16 discusses asymptotic theories which are often required to guarantee good properties of...
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Convergence Almost Sure
Order hidden in chaos: an erratic sequence of coin tosses exhibits a remarkable balance between heads and tails in the long run, at least “when the...
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Multidimensional Cubature Formulas with Superpower Convergence
AbstractIn many applications, multidimensional integrals over the unit hypercube arise, which are calculated using Monte Carlo methods. The...
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Straub’s Convergence Exists
AbstractIn his well-known monograph ‘‘Non-Life Insurance Mathematics’’ Erwin Straub proposed a new method for calculating IBNR-reserves, which he...
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Statistical Fibonacci convergence of complex uncertain variables
This paper presents several statistical convergence concepts of complex uncertain sequences based on a regular matrix of Fibonacci numbers:...
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Mosco convergence of set-valued supermartingale
The existence of regular martingale selectors for multivalued supermartingales with unbounded values in a separable Banach space Y is proved. In...
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Convergence of Random Fuzzy Sets
As in Chapter 5, we view random fuzzy sets as generalizations of random closed sets on R d , or more generally on...
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Correction to: On statistical convergence and strong Cesàro convergence by moduli
We correct a logic mistake in our paper “On statistical convergence and strong Cesàro convergence by moduli” (León-Saavedra et al. in J. Inequal....
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Modes of convergence of random variables and algebraic genericity
Important probabilistic problems require to find the limit of a sequence of random variables. However, this limit can be understood in different ways...
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Convergence of Sequences of Functions
This chapter investigates pointwise and uniform convergence of sequences and series of functions including many examples. Once the main results and...
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Almost Sure Convergence of Moment-Based Estimators
In the following, we investigate the moment-based problem, cf. (1.10), especially the so far unexamined almost sure convergence. The whole chapter is...
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Convergence in Conformal Field Theory
Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author...
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Rings Generated by Convergence Sets of Multidimensional Complete Field
The convergence sets of a multidimensional complete field are those having the property that all power series over it converge when substituting an...
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Global Approximations of Vector Optimization Problems in Terms of Variational Convergence
Global approximations of scalar optimization problems in terms of variational convergence have been studied for several decades. However, there are...
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Voronovskaja formula for Aldaz–Kounchev–Render operators: uniform convergence
The Voronovskaja formula for Aldaz–Kounchev–Render operators was established in terms of pointwise convergence. For suitable functions we prove it...