Change detection is a fundamental problem arising in many fields of engineering, in finance, in the natural and social sciences, and even in the humanities. This book is concerned with the problem of change detection within a specific context. In particular, the framework considered here is one in which changes are manifested in the statistical behavior of quantitative observations, so that the problem treated is that of statistical change detection. Moreover, we are interested in the on–line problem of quickest detection, in which the objective is to detect changes in real time as quickly as possible after they occur. And, finally, our focus is on formulating such problems in such a way that optimal procedures can be sought and found using the tools of stochastic analysis.

Thus, the purpose of this book is to provide an exposition of the extant theory underlying the problem of quickest detection, with an emphasis on providing the reader with the background necessary to begin new research in the field. It is intended both for those familiar with basic statistical procedures for change detection who are interested in understanding these methods from a fundamental viewpoint (and possibly extending them to new applications), and for those who are interested in theoretical questions of change detection themselves.

The approach taken in this book is to cast the problem of quickest detection in the framework of optimal stopping theory.