Counterexamples in Probability, 2nd Edition

Counterexamples (in the mathematical sense) are powerful tools of mathematical theory. This book covers counterexamples from probability theory and stochastic processes. This new expanded edition includes many examples and the latest research results. The author is regarded as one of the foremost experts in the field. Contains numbers examples. Following the success of the first edition, widely regarded as the classic reference work on the subject, Professor Stoyanov has expanded his work to include many new counterexamples and the latest research results. Nearly 300 counterexamples are included, selected for their interest and for the importance of the theory they illustrate. A summary of definitions and main results is provided at the beginning of each section, followed by counterexamples in order of content and difficulty. These counterexamples demonstrate the power and non-triviality of stochastics. They cover the main results used in undergraduate and graduate courses in probability and stochastic processes and provide new starting points for students, teachers and researchers. Lecturers and examiners will find these counterexamples a useful source of illustrations and ideas. Clases Of Random Events And Probabilities -- Classes Of Random Events -- Independence Of Random Events -- Random Variables And Basic Characteristics -- Distribution Functions Of Random Variables -- Expectations And Conditional Expectations -- Characteristic And Generating Functions -- Infinitely Divisible And Stable Distributions -- The Moment Problem -- Diverse Properties Of Random Variables -- Limit Theorems -- Laws Of Large Numbers -- Weak Convergence Of Probability Measures And Distributions. Stochastic Processes -- Basic Notions On Stochastic Processes -- Markov Processes -- Poisson Process And Wiener Process -- Supplementary Remarks -- References -- Index. Jordan M. Stoyanov. Includes Bibliographical References (p.317-338) And Index. This expanded edition includes many new examples and latest research results. Counterexamples (in the usual mathematical sense) are powerful tools of mathematical theory. This book contains counterexamples from probability theory and stochastic processes. Let  be an arbitrary non-empty set. Its elements, denoted by , will be interpreted as outcomes (results) of some experiment.