Linear Decomposition and Anticipating Integral for Certain Random Variables

The Almost Sure Convergence for Weighted Sums of Linear Negatively Dependent Random Variables

In this paper, we generalize a theorem of Shao [12] by assuming that is a sequence of linear negatively dependent random variables. Also, we extend some theorems of Chao [6] and Thrum [14]. It is shown by an elementary method that for linear negatively dependent identically random variables with finite -th absolute moment the weighted sums converge to zero as where and is an array of...

Moment inequalities for sums of certain independent symmetric random variables

This paper gives upper and lower bounds for moments of sums of independent random variables (Xk) which satisfy the condition that P (|X|k ≥ t) = exp(−Nk(t)), where Nk are concave functions. As a consequence we obtain precise information about the tail probabilities of linear combinations of independent random variables for which N(t) = |t| for some fixed 0 < r ≤ 1. This complements work of Glus...

Dominated Convergence for Fuzzy Random Variables

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...

Maximal Inequalities for Associated Random Variables

In a celebrated work by Shao [13] several inequalities for negatively associated random variables were proved. In this paper we obtain some maximal inequalities for associated random variables. Also we establish a maximal inequality for demimartingales which generalizes and improves the result of Christofides [4].