An Invariance Principle for Certain Dependent Sequences
Charles M. Newman,A. L. Wright +1 more
TLDR
In this article, it was shown that the associated random variables of a strictly stationary second order sequence can be associated, such that any two coordinatewise nondecreasing functions of the $X_i$'s are nonnegatively correlated.Abstract:
Let $X_1, X_2, \cdots$ be a strictly stationary second order sequence which is "associated"; i.e., is such that any two coordinatewise nondecreasing functions of the $X_i$'s (of finite variance) are nonnegatively correlated. If $\sum_j \operatorname{Cov}(X_1, X_j) < \infty$, then the partial sum processes, $W_n(t)$, defined in the usual way so that $W_n(m/n) = (X_1 + \cdots + X_m - mE(X_1))/\sqrt n$ for $m = 1, 2, \cdots$, converge in distribution on $C\lbrack 0, T\rbrack$ to a Wiener process. This result is based on two general theorems concerning associated random variables which are of independent interest.read more
Citations
More filters
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Journal ArticleDOI
Oriented Percolation in Two Dimensions
TL;DR: A self-contained survey of most of the results known about oriented percolation can be found in this article, along with a discussion of some of the most important topics. But this survey is limited to oriented percoding.
Book ChapterDOI
Asymptotic independence and limit theorems for positively and negatively dependent random variables
Book
Long Range Dependence
TL;DR: The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested, including connections with non-stationary processes.
Journal ArticleDOI
A Comparison Theorem on Moment Inequalities Between Negatively Associated and Independent Random Variables
TL;DR: The comparison theorem on moment inequalities between negatively associated and independent random variables extends the Hoeffding inequality on the probability bounds for the sum of a random sample without replacement from a finite population as discussed by the authors.
References
More filters
Book
Convergence of Probability Measures
TL;DR: Weak Convergence in Metric Spaces as discussed by the authors is one of the most common modes of convergence in metric spaces, and it can be seen as a form of weak convergence in metric space.
Journal ArticleDOI
An Introduction to Probability Theory and Its Applications.
Journal ArticleDOI
Convergence of Probability Measures
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Book ChapterDOI
Some Concepts of Dependence
TL;DR: In this article, the authors give three successively stronger definitions of positive dependence, and investigate their consequences, explore the strength of each definition through a number of examples, and give some statistical applications.