Basic Concepts from Probability Theory
This chapter reviews some basic material. We collect some elementary concepts and properties in connection with random variables, expected values, multivariate and conditional distributions. Then we define stochastic processes, both discrete and continuou
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Uwe Hassler
Stochastic Processes and Calculus An Elementary Introduction with Applications
Springer Texts in Business and Economics
More information about this series at http://www.springer.com/series/10099
Uwe Hassler
Stochastic Processes and Calculus An Elementary Introduction with Applications
123
Uwe Hassler Faculty of Economics and Business Administration Goethe University Frankfurt Frankfurt, Germany
ISSN 2192-4333 ISSN 2192-4341 (electronic) Springer Texts in Business and Economics ISBN 978-3-319-23427-4 ISBN 978-3-319-23428-1 (eBook) DOI 10.1007/978-3-319-23428-1 Library of Congress Control Number: 2015957196 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2016 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, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www.springer.com)
I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me. ISAAC NEWTON
Quoted from the novel Beyond Sleep by Willem Frederik Hermans
Preface
Over the past decades great importance has been placed on stochastic calculus and processes in mathematics, finance, and econometrics. This book addresses particularly readers from these fields, although students of other subjects as biology, engineering, or physics may find it useful, too.
Scope of the Book By now there exist a number of books describing stochastic integrals and stochastic calculus in an accessible manner. Such introductory books, however, typically address an audience having previous knowledge about and interest in one of the following three fields exclusively: finance, econometrics, or mathematics. The textbook at hand attempts to provide an introduction into stochastic calculus
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