The Strong Law of Large numbers

The aim of this work is to investigate results on almost sure convergence of weighted sums of coordinatewise pairwise negatively quadrant dependent random variables taking values in Hilbert spaces. As an application, the almost sure convergence of degenerate von Mises-statistics is investigated.

12p viambani 18-06-2024 1 1   Download

Lecture Probability Theory - Lecture 13: The Weak Law and the Strong Law of Large numbers. In this lecture, we will discuss limit theorems, Chebyshev’s inequality, and convergence “in probability”.

15p cucngoainhan0 10-05-2022 4 1   Download

In this report we present some noncommutative weak and strong laws of large numbers. Two case are considered: a von Neumann algebra with a normal faithful state on it and the algebra of measurable operators with normal faithful trace. 1. Introduction and notations One of the problems occurring in noncommutative probability theory concerns the extension of various results centered around limit theorems to the noncommutative context.

9p tuanlocmuido 19-12-2012 57 2   Download

Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2011, Article ID 279754, 13 pages doi:10.1155/2011/279754 Research Article On Strong Law of Large Numbers for Dependent Random Variables Zhongzhi Wang Faculty of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243002, China Correspondence should be addressed to Zhongzhi Wang, wzz30@ahut.edu.cn Received 16 December 2010; Accepted 3 March 2011 Academic Editor: Vijay Gupta Copyright q 2011 Zhongzhi Wang.

13p dauphong13 09-02-2012 43 5   Download