One service mathematics has rendered the 'Bt mm, ... si j'avait su comment en revenir, human race. It has put common sense back je n'y serais point alIe.' Jules Verne where it belongs. on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. O. Heavisidc Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a...

This book is devoted to an investigation of some important problems of mod ern filtering theory concerned with systems of 'any nature being able to per ceive, store and process an information and apply it for control and regulation'. (The above quotation is taken from the preface to 27]). Despite the fact that filtering theory is l'argely worked out (and its major issues such as the Wiener-Kolmogorov theory of optimal filtering of stationary processes and Kalman-Bucy recursive filtering theory have become classical) a development of the theory is far from complete. A great deal of recent...

In this volume the investigations of filtering problems, a start on which has been made in 55], are being continued and are devoted to theoretical problems of processing stochastic fields. The derivation of the theory of processing stochastic fields is similar to that of the theory extensively developed for stochastic processes ('stochastic fields with a one-dimensional domain'). Nevertheless there exist essential distinctions between these cases making a construction of the theory for the multi-dimensional case in such a way difficult. Among these are the absence of the notion of the...