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Random Variables
Random variables are the central objects of study in probability. The name ‘random variables’ is somewhat of a misnomer since they are neither random...
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Discrete Random Variables
The number of heads in a sequence of 10,000 coin tosses, the number of days it takes until the next rain and the size of a genealogical tree are...
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Random Variables and Their Probability Distributions
Chapter 5 defines the random variables and their probability distributions. Many properties such as mean,...
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Extended Acceptable Random Variables and Hoeffding Inequalities
AbstractThe concept has of acceptable random variables been applied to exponential inequalities for the partial sums by so many authors in different...
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Uncertainty quantification for random domains using periodic random variables
We consider uncertainty quantification for the Poisson problem subject to domain uncertainty. For the stochastic parameterization of the random...
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Measurable Functions and Random Variables
To study random variable in a more general setting, we introduce the notion of measurable functions. In probability theory, a random variable is a...
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Sums of Independent Random Variables
In this chapter we collect basic definitions and results on the normal approximation of distributions of independent random variables (in Kolmogorov...
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On Normalization of Integer-Valued Random Variables
The notion of general families of thinning operators is proposed. The main goal of such notion is to allow normalization of integer-valued random...
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Random variables and their quantitative characteristics
In the second chapter random variables are introduced and investigated in the framework of axiomatic of Kolmogorov. It is shown a connection of...
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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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Random polynomials in several complex variables
We generalize some previous results on random polynomials in several complex variables. A standard setting is to consider random polynomials
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Complete moment convergence for ND random variables under the sub-linear expectations
In this article, we establish a general result on complete moment convergence for arrays of rowwise negatively dependent(ND) random variables under...
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Beyond Discrete and Continuous Random Variables
We provide several examples of singular distributions and review the definition and basic properties of the Riemann–Stieltjes integral. By using the...
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Properties of complex-valued power means of random variables and their applications
We consider power means of independent and identically distributed (i.i.d.) non-integrable random variables. The power mean is an example of a...
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Continuous random variables
The discrete random variables we’ve met up to now have been restricted to distinct values that are separated by gaps, such as integers 0, 1, 2, : :...
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Weak convergence of sequences of random variables
The chapter four is devoted in a systematic study of a weak convergence of sequences of random variables. It is shown the equivalence between a weak...
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Revisiting the Product of Random Variables
For a large class of distribution functions we study properties of the product of random variables X and Y . We take into account the dependency...
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Expectations and convergence of sequences of random variables
In the third chapter asymptotic properties of sequences of random variables are studied. Lemma of Fatou and the Lebesgue dominated convergence...
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Strong convergence for weighted sums of WOD random variables and its application in the EV regression model
The strong convergence for weighted sums of widely orthant dependent (WOD) random variables is investigated. As an application, we further...