Definition of information and entropy in the absence of noise
In modern science, engineering and public life, a big role is played by information and operations associated with it: information reception, information transmission, information processing, storing information and so on. The significance of information
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Theory of Information and its Value Edited by Roman V. Belavkin Panos M. Pardalos · Jose C. Principe
Theory of Information and its Value
Roman V. Belavkin • Panos M. Pardalos Jose C. Principe Editors
Theory of Information and its Value
Editors Roman V. Belavkin Faculty of Science and Technology Middlesex University London, UK
Panos M. Pardalos Industrial and Systems Engineering University of Florida Gainesville, FL, USA
Jose C. Principe Electrical & Computer Engineering University of Florida Gainesville, FL, USA Author Ruslan L. Stratonovich (Deceased)
ISBN 978-3-030-22832-3 ISBN 978-3-030-22833-0 (eBook) https://doi.org/10.1007/978-3-030-22833-0 Mathematics Subject Classification: 94A17, 94A05, 60G35 © Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG. The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword
It would be impossible for us to start this book without mentioning the main achievements of its remarkable author, Professor Ruslan Leontievich Stratonovich (RLS or Ruslan later). He was a brilliant mathematician, probabilist and theoretical physicist, best known for the development of the symmetrized version of stochastic calculus (an alternative to Itˆo calculus), with stochastic differential equations and integrals now bearing his name. His unique and beautiful approach to stochastic processes was invented in the 1950s during the time of his doctoral work on the solution to the notorious nonlinear filtering problem. The importance of this work was immediately recognized by the great Andrei Kolmogorov, who invited Ruslan, then a graduate student, for a discussion of his first papers. This work was so much ahead of its time that its initial reception in the Soviet mathematical communit
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