Counterexamples in Probability (Wiley Series in Probability and Statistics) - gebunden oder broschiert

Counterexamplesin Probability Second Edition Jordan M. Stoyanov Bulgarian Academy of Sciences and University of Sofia 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. Contents Preface to the Second Edition Preface to the First Edition Basic Notation and Abbreviations Part 1 Classes of Random Events and ProbabilitiesClasses of Random EventsProbabilitiesIndependence of Random EventsDiverse Properties of Random Events and their ProbabilitiesPart 2 Random Variables and Basic CharacteristicsDistribution Functions of Random VariablesExpectations and Conditional ExpectationsIndependence of Random VariablesCharacteristic and Generating FunctionsInfinitely Divisible and Stable DistributionsNormal DistributionThe Moment ProblemCharacterization Properties of Some Probability DistributionsDiverse Properties of Random VariablesPart 3 LimitTheoremsVarious Kinds of Convergence of Sequences of Random VariablesLaws of Large NumbersWeak Convergence of Probability Measures and DistributionsCentral Limit TheoremDiverse Limit TheoremsPart 4 Stochastic ProcessesBasic Notions on Stochastic Proce