DEPENDENCE IN PROBABILITY AND STATISTICS:
A Survey of Recent Results
Birkhäuser, Boston, 1986
ISBN 0-8176-3323-5, 473 pages,
The classical limit results of probability theory and statistics were obtained under the assumption that the observed variables are independent. From the point of view of mathematical analysis this is the simplest case to be studied. Often, however, independence is an idealization. More realistic models admit some dependence; in fact, in many models, dependence between the variables is the essential fact.
In recent years our understanding of dependence structures and in particular of limiting procedures under dependence assumptions has improved enormously.Various degrees of weak and strong dependence are studied, ranging from mixing conditions and martingale structures to long-range dependence. Central and non-central limit theorems, invariance principles, laws of the iterated logarithm, and results relating to extreme values are among the limit results treated.
This book on dependence will serve as a basic reference to researchers in probability and statistics.
Table of Contents (in Postcript)