Stochastic Comparisons of Some Distances between Random Variables

Stochastic Comparisons of Weighted Sums of Arrangement Increasing Random Variables

Assuming that the joint density of random variables X1, X2, . . . , Xn is arrangement increasing (AI), we obtain some stochastic comparison results on weighted sums of Xi’s under some additional conditions. An application to optimal capital allocation is also given. Mathematics Subject Classifications (2000): 60E15; 62N05; 62G30

SOME PROBABILISTIC INEQUALITIES FOR FUZZY RANDOM VARIABLES

In this paper, the concepts of positive dependence and linearlypositive quadrant dependence are introduced for fuzzy random variables. Also,an inequality is obtained for partial sums of linearly positive quadrant depen-dent fuzzy random variables. Moreover, a weak law of large numbers is estab-lished for linearly positive quadrant dependent fuzzy random variables. Weextend some well known inequ...

SOME RESULTS OF MOMENTS OF UNCERTAIN RANDOM VARIABLES

Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable...

Random Variables and Stochastic Processes

Stochastic relations of random variables and processes

This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov processes, it suffices that the generators of the processes preserve some, not necessarily reflexive or transitive, subrelation of the order relation. The m...