Counterexamples in Probability: Third Edition (Dover Books on Mathematics) by Jordan M. Stoyanov (PDF)

Description

Most mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement’s falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study as well as valuable tools for teaching, learning, and research. This third edition of the definitive book on counterexamples in probability and stochastic processes presents the author’s revisions and corrections in addition to a substantial new appendix. Suitable as a supplementary source for advanced undergraduates and graduate courses in the field of probability and stochastic processes, this volume features a wide variety of topics that are challenging in both content and detail. The text consists of four chapters and twenty-five sections. Each section begins with short introductory notes of basic definitions and main results. Counterexamples related to the main results follow, along with motivation for questions and counterstatements that range in difficulty. A familiarity with basic notions and results in probability and stochastic processes is assumed, and a chapter of supplementary remarks provides a wealth of information about original sources as well as references for further studies.

User’s Reviews

Editorial Reviews: About the Author Formerly a Senior Research Fellow at the Bulgarian Academy of Sciences and a Professor at the University of Sofia, Jordan Stoyanov is on the faculty of the School of Mathematics and Statistics, University of Newcastle, United Kingdom.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This is the third edition of the book. The first two editions were published by Wiley. Now, finally we have this wonderful book as a paperback from Dover, at a very affordable price.The author of the book has collected in one volume hundreds of examples from textbooks, monographs, and original papers of numerous authors. The examples are well organized, with explanations in each section, setting up the scene, giving the big picture, and explaining the motivation behind the questions that the counterexamples answer. There is an extensive bibliography pointing to the origins of the examples and suggesting further reading. I am truly impressed by the breadth of the material, by the sheer amount of work that must have gone into this project.The level of the counterexamples range from the very simple to the highly technical. Thus, everybody studying or teaching Probability will find something in this book to enjoy. From the novice to the sophisticated mathematician working in that field, everyone will find new information, new things to learn. This being said, it should be noted that the book requires a certain degree of proficiency with Probability. The writing is clear, but terse at times, and requires the reader to be willing to follow the calculations with a pencil and paper. More advanced readers will probably get more out of the book than laymen, but there is truly something for everybody in this little book.As an interesting aside, the book includes several (four or five) pictures from A.T.Fomenko, the Russian mathematician who became famous for his work in Minimal Surfaces and for his mathematics-inspired art (and, more recently, infamous for his revision of chronology). The pictures included are not directly related to the text, but are math-inspired and create an interesting ambiance.

⭐Less painful way to learn probability theory and stochastic processes (martingales, Poisson processes, Markov chains, Borel spaces, Brownian motion) than other texts I have attempted.

⭐Following the successful “Counterexamples in Topology”, lots of good math books that begin with “Counterexample in” should be tried, but this is one of the very few so far. The book deserves praise for that. The bad news is that the discussion is extremely technical and many of the examples don’t feel very “counter”. This is some inside baseball for hardcore probabilists. It would be nice to see a more inspired, more accessible effort.

⭐This is an excellent book written by a world renowned probabilist. I recommend it to all graduate students and researchers in analysis and probability. It is a critical approach in studying probability and measure theory.

⭐As described, thanks

⭐A must have for anybody who want to learn probability in some depth.

⭐Very well written.

⭐Thank you!

⭐This book is a gem with lot a of very useful counterexamples that really help to understand the theory of Probability. The author must commended for his patience and resilience in collecting all these counterexamples. Highly recommended.

⭐the layout is poor but the content is very interesting: overall for university teachers it provides interesting examples. The only thing I complain about is the layout that

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