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Proceedings of the Norbert Wiener Centenary Congress, 1994 (East Lansing, Michigan, 1994) 51 Louis H http://dx.doi.org/10.1090/psapm/052 Selected Titles in This Series 52 V. Mandrekar and P. R. Masani, editors, Proceedings of the Norbert Wiener Centenary Congress, 1994 (East Lansing, Michigan, 1994) 51 Louis H. Kauffman, editor, The interface of knots and physics (San Francisco, California, January 1995) 50 Robert Calderbank, editor, Different aspects of coding theory (San Francisco, California, January 1995) 49 Robert L. Devaney, editor, Complex dynamical systems: The mathematics behind the Mandlebrot and Julia sets (Cincinnati, Ohio, January 1994) 48 Walter Gautschi, editor, Mathematics of Computation 1943-1993: A half century of computational mathematics (Vancouver, British Columbia, August 1993) 47 Ingrid Daubechies, editor, Different perspectives on wavelets (San Antonio, Texas, January 1993) 46 Stefan A. Burr, editor, The unreasonable effectiveness of number theory (Orono, Maine, August 1991) 45 De Witt L. Sumners, editor, New scientific applications of geometry and topology (Baltimore, Maryland, January 1992) 44 Bela Bollobas, editor, Probabilistic combinatorics and its applications (San Francisco, California, January 1991) 43 Richard K. Guy, editor, Combinatorial games (Columbus, Ohio, August 1990) 42 C. Pomerance, editor, Cryptology and computational number theory (Boulder, Colorado, August 1989) 41 R. W. Brockett, editor, Robotics (Louisville, Kentucky, January 1990) 40 Charles R. Johnson, editor, Matrix theory and applications (Phoenix, Arizona, January 1989) 39 Robert L. Devaney and Linda Keen, editors, Chaos and fractals: The mathematics behind the computer graphics (Providence, Rhode Island, August 1988) 38 Juris Hartmanis, editor, Computational complexity theory (Atlanta, Georgia, January 1988) 37 Henry J. Landau, editor, Moments in mathematics (San Antonio, Texas, January 1987) 36 Carl de Boor, editor, Approximation theory (New Orleans, Louisiana, January 1986) 35 Harry H. Panjer, editor, Actuarial mathematics (Laramie, Wyoming, August 1985) 34 Michael Anshel and William Gewirtz, editors, Mathematics of information processing (Louisville, Kentucky, January 1984) 33 H. Peyton Young, editor, Fair allocation (Anaheim, California, January 1985) 32 R. W. McKelvey, editor, Environmental and natural resource mathematics (Eugene, Oregon, August 1984) 31 B. Gopinath, editor, Computer communications (Denver, Colorado, January 1983) 30 Simon A. Levin, editor, Population biology (Albany, New York, August 1983) 29 R. A. DeMillo, G. I. Davida, D. P. Dobkin, M. A. Harrison, and R. J. Lipton, Applied cryptology, cryptographic protocols, and computer security models (San Francisco, California, January 1981) 28 R. Gnanadesikan, editor, Statistical data analysis (Toronto, Ontario, August 1982) 27 L. A. Shepp, editor, Computed tomography (Cincinnati, Ohio, January 1982) 26 S. A. Burr, editor, The mathematics of networks (Pittsburgh, Pennsylvania, August 1981) 25 S. I. Gass, editor, Operations research: mathematics and models (Duluth, Minnesota, August 1979) 24 W. F. Lucas, editor, Game theory and its applications (Biloxi, Mississippi, January 1979) (Continued in the back of this publication) Norbert Wiener 1894-1964 Photograph taken in 1963 in Madison, Wisconsin. Proceedings of the Norbert Wiener Centenary Congress, 1994 Proceedings of Symposia in APPLIED MATHEMATICS Volume 52 Proceedings of the Norbert Wiener Centenary Congress, 1994 Michigan State University November 27-December 3, 1994 V. Mandrekar P. R. Masani Editors S, American Mathematical Society a Providence, Rhode Island ^NDED 1991 Mathematics Subject Classification. Primary 60H30, 42A38, 94A05, 31C15, 81P20; Secondary 60G46, 60H05, 94A15. Library of Congress Cataloging-in-Publication Data Norbert Wiener Centenary Congress (1994 : Michigan State University) Proceedings of the Norbert Wiener Centenary Congress, 1994 : Michigan State University, November 27-December 3, 1994 / V. Mandrekar, P. R. Masani, editors. p. cm.—(Proceedings of symposia in applied mathematics, ISSN 0160-7634 ; v. 52) Includes bibliographical references. ISBN 0-8218-0452-9 (alk. paper) 1. Stochastic analysis—Congresses. 2. Fourier analysis—Congresses. I. Mandrekar, V. (Vid- yadhar), 1939- . II. Masani, Pesi Rustom. III. Title. IV. Series. QA274.2.N67 1994 519.2—dc20 96-43346 CIP Copying and reprinting. Material in this book may be reproduced by any means for educational and scientific purposes without fee or permission with the exception of reproduction by services that collect fees for delivery of documents and provided that the customary acknowledgment of the source is given. This consent does not extend to other kinds of copying for general distribution, for advertising or promotional purposes, or for resale. Requests for permission for commercial use of material should be addressed to the Assistant to the Publisher, American Mathematical Society, P. O. Box 6248, Providence, Rhode Island 02940-6248. Requests can also be made by e-mail to reprint-permissionQams.org. Excluded from these provisions is material in articles for which the author holds copyright. In such cases, requests for permission to use or reprint should be addressed directly to the author(s). (Copyright ownership is indicated in the notice in the lower right-hand corner of the first page of each article.) © 1997 by the American Mathematical Society. All rights reserved. The American Mathematical Society retains all rights except those granted to the United States Government. Printed in the United States of America. @ The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. 10 9 8 7 6 5 4 3 2 1 02 01 00 99 98 97 Norbert Wiener Centenary Congress November 27, 1994 to December 3, 1994 Michigan State University Department of Statistics and Probability Michigan State University East Lansing, Michigan co-sponsored by the American Mathematical Society, International Association of Cybernetics, and World Organization of Systems and Cybernetics Organizing Committee J. Benedetto (University of Maryland) D. L. Burkholder (University of Illinois, AMS representative) T. Kailath (Stanford University) G. Kallianpur (University of North Carolina) V. Mandrekar (Michigan State University) P. R. Masani (University of Pittsburgh and WOSC representative) S. Mitter (MIT) I. E. Segal (MIT) Local Organizers Raoul LePage and V. Mandrekar Supporters National Science Foundation Army Research Office Capital Area Community Foundation Institute of Mathematics and Applications Deutsche Forschungsge Meinshaft French Academy of Sciences Osterreichische Studiengesellschaft Fur Kybernetik Royal Netherlands Academy of Arts and Sciences The Royal Society The Swedish Academy of Engineering Sciences Swiss Academy of Sciences vii Contributors D. R. Adams, Professor of Mathematics, University of Kentucky S. Albeverio, Lehrstuhl Fakultat und Inst it ut fiir Mathematik, Ruhr-Universitat Bochum H. Bart, Professor of Mathematics, Economic Institute, Erasmus University, Rotterdam J. R. Benedetto, Professor of Mathematics, University of Maryland N. K. Bose, HRB Systems Professor, and Director, The Spatial and Temporal Processing Center, The Pennsylvania State University D. L. Burkholder, Professor of Mathematics, Center for Advanced Study, University of Illinois E. H. Carlen, Associate Professor of Mathematics, Georgia Institute of Technology, Atlanta H. A. Feichtinger, Professor of Mathematics, University of Vienna G. D. Gale, Professor of Philosophy, University of Missouri-Kansas City /. Gohberg, Professor of Mathematics, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University L. Gross, Professor of Mathematics, Cornell University M. A. Kaashoek, Professor of Mathematics, Vrije University G. Kallianpur, Alumni Distinguished Professor of Statistics, Center for Stochastic Processes, University of North Carolina, Chapel Hill J. R. Klauder, Professor of Mathematics, University of Florida P. Malliavan, l'Academie des Sciences, Paris R. W. Mann, Whitaker Professor of Biomedical Engineering Emeritus Massachus• etts Institute of Technology P. R. Masani, University Professor, Department of Mathematics and Statistics, University of Pittsburgh B. McMillan, Formerly Vice President, Bell Telephone Laboratories S. A. Molchanov, Professor of Mathematics, University of North Carolina, Charlotte, formerly Professor of Mathematics and Statistics, Moscow State University 0. Penrose, F.R.S., Professor of Mathematics Emeritus, Herriot-Watt University, Edinburgh K. H. Pribram, James P. and Anna King University Professor and Eminent Scholar, Commonwealth of Virginia, Radford University, and Professor Emeritus, Stanford University ix x CONTRIBUTORS J. Rissanen, Professor of Mathematics, Technical University of Tempere, Finland, and member of Research Staff, IBM Almaden Center D. Roseman, Professor of Mathematics, University of Iowa /. E. Segal, Professor of Mathematics Emeritus, Massachusetts Institute of Technology H. A. Stapp, Senior Staff Physicist, Lawrence Berkeley Laboratories, University of California E. G. F. Thomas, Professor of Mathematics, University of Groningen R. L. Wornock, Visiting Physicist, formerly Staff Physicist, Stanford Linear Accel• erator Center S. Watanabe, Professor of Mathematics, Kyoto University Contents Norbert Wiener Centenary Congress: Sponsors, organizing comittee and supporters vii List of contributors ix Preface: Overview of the Norbert Wiener Centenary Congress and acknowledgment by the editors xv Program xlv I. Wiener's Concept of the Stochastic Universe. Wiener-Kolmogorov
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