All macroscopic physical systems are subject to fluctuations or noise. One of the most useful and interesting developments in modern statistical mechanics has been the realization that even complex nonequilibrium systems can often be reduced to equivalent ones of only a few degrees of freedom by the elimination of dynamically nonrelevant variables. Theoretical descriptions of such contracted systems necessarily begin with a set of either continuous or discrete dynamical equations which can then be used to describe noise driven systems with the inclusion of random terms. Studies of these stochastic dynamical equations have expanded rapidly in the past two decades, so that today an exuberant theoretical activity, a few experiments, and a remarkably large number of applications, some with challenging technological implications, are evident.

The purpose of these volumes is twofold. First we hope that their publication will help to stimulate new experimental activity by contrasting the smallness of the number of existing experiments with the many research opportunities raised by the chapters on applications. Secondly, it has been our aim to collect together in one place a complete set of authoritative reviews with contributions representative of all the major practitioners in the field. We recognize that as an inevitable consequence of the intended comprehensiveness, there will be few readers who will wish to digest these volumes in their entirety. We trust, instead, that readers will be stimulated to choose from the many possibilities for new research represented herein, and that they will find all the specialized tools, be they experimental or theoretical, that they are likely to require.