Jordan M. Stoyanov - Counterexamples in Probability Third Edition (Dover Books on Mathematics), 3d edition

ABOUT THE AUTHOR

Jordan Stoyanov was born in Bulgaria and his alma mater is Moscow State University, where he studied mathematics and earned degrees in probability theory as one of the scientific sons of Albert Shiryaev.

He has published a series of paperson his own and with co-authorson a range of contemporary stochastic problems, and wrote five bookswhich have been published in several different languages and countries. He has also been an invited speaker at several international forums, and has served on editorial boards of professional journals.

He has been a visiting professor at universities in Europe and America, has taught standard and non-standard courses, and has supervised a number of students for MSc and PhD degrees. He spent the last 15 years in the UK holding a position at Newcastle University.

He recently retired, and now enjoys life and hobbies, among them research, travels, seminar talks, meeting good people and seeing extra-ordinary places all over the world. He values a sense of humor, enjoys difficult things, and accepts the challenge of sometimes adopting an unusual positionwhether in everyday life or professionally.

Over the last three decades the idea of using counterexamples in probability has been well-received by people involved in learning, teaching, and research. Stoyanovs contributions in this field have won praise from both his peers and students.

Counterexamples in

PROBABILITY

THIRD EDITION

Courtesy of Professor A. T. Fomenko of Moscow University.

Counterexamples in

PROBABILITY

THIRD EDITION

Jordan M. Stoyanov

Formerly at:

Newcastle University, Newcastle upon Tyne, United Kingdom

Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil

Northern Kentucky University, Highland Heights, Kentucky, USA

Universit Joseph Fourier, Grenoble, France

Miami University, Oxford, Ohio, USA

Queens University, Kingston, Ontario, Canada

Universit di Padova, Padova, Italy

Concordia University, Montral, Qubec, Canada

Sofia University St. Kliment Ohridski, Sofia, Bulgaria

Bulgarian Academy of Sciences, Sofia, Bulgaria

DOVER PUBLICATIONS, INC.

Mineola, New York

Copyright

Copyright 1987, 1997, 2013 by Jordan M. Stoyanov
All rights reserved.

Bibliographical Note

This Dover edition, first published in 2013, is a revised, corrected, and amended republication of the second edition of the work, originally published by John Wiley & Sons, Inc., Chichester and New York, in 1997 [First edition: 1987].

The publisher joins the author in thanking Venelin Chernogorov for his work in preparing the final files for publication. The illustrations are reprinted here with the generous permission of Prof. A. T. Fomenko.

Library of Congress Cataloging-in-Publication Data

Stoianov, Iordan, author.

Counterexamples in probability / Jordan M. Stoyanov, formerly at: Newcastle University, Newcastle upon Tyne, United Kingdom; Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brasil; Northern Kentucky University, Highland Heights, Kentucky, USA; Universit Joseph Fourier, Grenoble, France; Miami University, Oxford, Ohio, USA; Queens University, Kingston, Ontario, Canada; Universit di Padova, Padova, Italy; Concordia University, Montral, Qubec, Canada; Sofia University St. Kliment Ohridski, Sofia, Bulgaria; Bulgarian Academy of Sciences, Sofia, Bulgaria.Third edition.

pages cm

Summary: While most mathematical examples illustrate the truth of a statement, counterexamples demonstrate a statements falsity. Enjoyable topics of study, counterexamples are valuable tools for teaching, learning, and research. The definitive book on the subject in regards to probability and stochastic processes, this third edition features the authors revisions and corrections plus a substantial new appendix. 2013 editionProvided by publisher.

Includes bibliographical references and index.

eISBN-13: 978-0-486-31593-5

1. Probabilities. 2. Stochastic processes. I. Title.

QA273.S7535 2013

519.2dc23

2013030644

Manufactured in the United States by Courier Corporation

49998701 2013

www.doverpublications.com

To Lyubomira, Viktoria, Rosalie and Maya

Preface to the Third Edition

The Wiley editions, 1987 and 1997, and the Russian editions, 1999 and 2012, of the book received reasonable attention. Apart from some 25 reviews in scientific journals and several citations, the book was used effectively for courses and seminars in probability and also for comprehensive PhD exams at universities in USA. I was invited to universities in Europe and America to deliver special lectures on counterexamples and their role in teaching and research.

Leaving positive reactions aside, I was more concerned by letters and messages containing different sort of complaints.

Some colleagues were angrily asking why I had not used counterexamples from their papers and had not included the papers in the References. I apologized to all of them promising to correct this in the next edition.

Other colleagues were not happy about the Index and references for the examples because I had not provided the pages thus leaving the reader to do his/her own search in a book, journal, etc. Others, on the contrary, shared with me that exactly when digging in books they not only found the desired details but also discovered, e.g., how wonderful the books by A. Renyi, K.L. Chung, A.N. Shiryaev, R Billingsley and L.C.G. Rogers & D. Williams are.

Complaints came from readers who wanted to cite examples from the 2nd edition of my book in their papers, and needed to include the Mathematical Reviews data. But while the Ist edition was reviewed (see MR 89f:60001), strangely enough, the 2nd was not. Ask Mathematical Reviews to explain this mystery.

I received letters and messages from readers, mainly students, who liked the book in many ways but were unable to pay Wiley a price of 200 for a copy on demand or to Amazon a price of $250 and even more. I answered invariably: do not buy it, there will be a new edition with a reasonable price.

Finally, here is an episode that happened during the Joint Annual Meeting of AMS and MAA, January 1997, San Diego, California. I was there with a fresh copy of the 2nd Wiley edition, just published. Among those who showed a keen interest to my book was John Grafton, Senior Editor at Dover Publications, New York. Returning the book to me after perusing it for half an hour he said: One day I will publish this book at Dover! That day arrived.

Meanwhile, I accumulated a large amount of new material on old and new topics. In order to reflect these developments I prepared for the Dover edition a special Appendix containing key words followed by references. The main text of the 2nd Wiley edition was checked again, slightly revised, corrected and updated. As before, I followed the rule: Always pick the lightest item that still fits in the bag!

Despite some difficult years in the past, I have been a lucky man! My unusual life started from Divotino/Pernik (Bulgaria) and my later studies, work and travels brought me via Sofia and Moscow to Montreal, Paris, New York, Tokyo, Rio de Janeiro, Taipei and London. In one or another way, I was inspired in my work and life by remarkable people. I will only mention here a few names: Ivan Tiufekchiev, Albert N. Shiryaev, Constance Van Eeden, Fortunato Pesarin, Alain Le Breton, Paulo Ribenboim, Bart Braden, Masaaki Kijima and Gwo Dong Lin. I would like to use this opportunity to express my deep gratitude to all of them for their invariable support and precious help.