Maximal Inequalities for Dependent Random Variables and Applications
نویسنده
چکیده
For a sequence {Xn, n ≥ 1} of dependent square integrable random variables and a sequence {bn, n ≥ 1} of positive numbers, we establish a maximal inequality for weighted sums of dependent random variables. Applying this inequality, we obtain the almost sure convergence of ∑n i 1Xi/bi and ∑n i 1Xi/bn. Copyright q 2008 Soo Hak Sung. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
منابع مشابه
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].
متن کاملComplete Convergence and Some Maximal Inequalities for Weighted Sums of Random Variables
Let be a sequence of arbitrary random variables with and , for every and be an array of real numbers. We will obtain two maximal inequalities for partial sums and weighted sums of random variables and also, we will prove complete convergence for weighted sums , under some conditions on and sequence .
متن کاملSome Probability Inequalities for Quadratic Forms of Negatively Dependent Subgaussian Random Variables
In this paper, we obtain the upper exponential bounds for the tail probabilities of the quadratic forms for negatively dependent subgaussian random variables. In particular the law of iterated logarithm for quadratic forms of independent subgaussian random variables is generalized to the case of negatively dependent subgaussian random variables.
متن کاملRosenthal’s Type Inequalities for Negatively Orthant Dependent Random Variables
In this paper, we obtain some Rosenthal’s type inequalities for negatively orthant dependent (NOD) random variables.
متن کاملSOME 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...
متن کامل