Forward-convex convergence in probability of sequences of nonnegative random variables

FURTHER RESULTS OF CONVERGENCE OF UNCERTAIN RANDOM SEQUENCES

Convergence is an issue being widely concerned about. Thus, in this paper, we mainly put forward two types of concepts of convergence in mean and convergence in distribution for the sequence of uncertain random variables. Then some of theorems are proved to show the relations among the three convergence concepts that are convergence in mean, convergence in measure and convergence in distributio...

Limit theorems of probability theory : Sequences of independent random variables

The simple notion of statistical independence lies at the core of much that is important in probability theory. First there was the classical central limit theorem (CLT) of De Moivre and Laplace which, in its final form due to Paul Lévy, says that the sum Sn of n independent and identically distributed (i.i.d.) random variables Xj (1 ≤ j ≤ n) having finite second moments is asymptotically Gauss...

Dominated Convergence for Fuzzy Random Variables

Complete Convergence for Negatively Dependent Sequences of Random Variables

for all x, y ∈ R. Moreover, it follows that 1.2 implies 1.1 , and hence, 1.1 and 1.2 are equivalent. Ebrahimi and Ghosh 1 showed that 1.1 and 1.2 are not equivalent for a collection of 3 or more random variables. They considered random variables X1, X2, and X3 where X1, X2, X3 assumed the values 0, 1, 1 , 1, 0, 1 , 1, 1, 0 , and 0, 0, 0 each with probability 1/4. The random variables X1, X2, an...

Acceptable random variables in non-commutative probability spaces

Acceptable random variables are defined in noncommutative (quantum) probability spaces and some of probability inequalities for these classes  are obtained. These results are a generalization of negatively orthant dependent random variables in probability theory. Furthermore, the obtained results can be used for random matrices.