Random Variables and Distributions
Most quantities that we deal with every day are more or less of a random nature. The height of the person we first meet on leaving home in the morning, the grade we will earn in the next exam, the cost of a bottle of wine we will buy in the nearest shoppi
- PDF / 21,837,699 Bytes
- 323 Pages / 439 x 666 pts Page_size
- 109 Downloads / 273 Views
Springer-Verlag Berlin Heidelberg GmbH
Sasha Cyganowski Peter Kloeden Jerzy Ombach
FroITl EleITlentary Probability to Stochastic Differential Equations withMAPLE®
Springer
Library of Congress Cataloging-in Publication Data applied for Cyganowski, S.: From elementary probability to stochastic diff~rential equations with MAPLE I Sasha Cyganowski; Peter Kloeden; Jerzy Ombach. - Berlin; Heidelberg; New York; Barcelona; Hong Kong; London; Milan; Paris; Tokyo: Springer, 2002 (Universitext) ISBN 978-3-642-56144-3 (eBook) ISBN 978-3-540-42666-0 DOI 10.1007/978-3-642-56144-3 0101 deutsche buecherei
Mathematics Subject Classification (2000): 60-01,60-08
ISBN 978-3-540-42666-0 This work is subject to copyright. AII rights are reserved, 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 way, and storage in data' banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9. 1965. in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law.
@Springer-VerlagBerlinHeidelbergl00l Originally published by Springer-Verlag Berlin Heidelberg New York in 2002 The use of general descriptive names, registered names. trademarks. 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. Typesetting: Camera-ready copy produced by the authors using a Springer TEX macro package Cover design: design 6- production GmbH. Heidelberg Printed on acid-free paper
SPIN: 10850538
46/3141db - 5 4 3 1 1 o
Preface
Measure and integration were once considered, especially by many of the more practically inclined, to be an esoteric area of abstract mathematics best left to pure mathematicians. However, it has become increasingly obvious in recent years that this area is now an indispensable, even unavoidable, language and provides a fundamental methodology for modern probability theory, stochastic analysis and their applications, especially in financial mathematics. Our aim in writing this book is to provide a smooth and fast introduction to the language and basic results of modern probability theory and stochastic differential equations with help of the computer manipulator software package MAPLE. It is intended for advanced undergraduate students or graduates, not necessarily in mathematics, to provide an overview and intuitive background for more advanced studies as well as some practical skills in the use of MAPLE software in the context of probability and its applications. This book is not a conventional mathematics book. Like such books it provides precise definitions and mathematical statements, particularly those based on measure and integration theory, but instead of mathemat
