Counterexamples in Probability: Third Edition

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.