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Ernst Eberlein and Murad S. Taqqu, editors **

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* DEPENDENCE IN PROBABILITY AND STATISTICS:*

*A Survey of Recent Results*

Birkhäuser, Boston, 1986

ISBN 0-8176-3323-5,
473 pages,

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** **## ABSTRACT

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)

*Murad Taqqu *

Sun September 10, 1998