Counterexamples in Probability (Wiley Series in Probability and Statistics)

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9780471916499: Counterexamples in Probability (Wiley Series in Probability and Statistics)
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Counterexamples (in the usual mathematical sense) are powerful tools of mathematical theory. In this book the author gives more than 250 drawn from the whole field of probability theory and stochastic processes. The counterexamples are selected for their interest and for the importance of the theory they illustrate. Each section starts with a summary of definitions and main results, followed by counterexamples ordered by content and difficulty. Full references and additional sources are given. These counterexamples serve to illustrate the power, beauty and non-triviality of stochastics. They will provide new starting points for students and their teachers, as well as for researchers. The main results used in undergraduate and graduate courses in probability and stochastic processes are covered by these counterexamples. They will provide a useful source of illustrations and ideas for lecturers and examiners, as well as valuable supplementary reading for students.

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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.

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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 Probabilities

  1. Classes of Random Events
  2. Probabilities
  3. Independence of Random Events
  4. Diverse Properties of Random Events and their Probabilities
Part 2 Random Variables and Basic Characteristics
  1. Distribution Functions of Random Variables
  2. Expectations and Conditional Expectations
  3. Independence of Random Variables
  4. Characteristic and Generating Functions
  5. Infinitely Divisible and Stable Distributions
  6. Normal Distribution
  7. The Moment Problem
  8. Characterization Properties of Some Probability Distributions
  9. Diverse Properties of Random Variables
Part 3 Limit Theorems
  1. Various Kinds of Convergence of Sequences of Random Variables
  2. Laws of Large Numbers
  3. Weak Convergence of Probability Measures and Distributions
  4. Central Limit Theorem
  5. Diverse Limit Theorems
Part 4 Stochastic Processes
  1. Basic Notions on Stochastic Processes
  2. Markov Processes
  3. Stationary Processes and Some Related Topics
  4. Discrete-Time Martingales
  5. Continuous-Time Martingales
  6. The Poisson Process and the Wiener Process
  7. Diverse Properties of Stochastic Processes
Supplementary Remarks References Index

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9780471965381: Counterexamples in Probability, 2nd Edition

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ISBN 10:  0471965383 ISBN 13:  9780471965381
Publisher: Wiley, 1997
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Stoyanov, Jordan M.
Published by John Wiley & Sons Inc (1988)
ISBN 10: 0471916498 ISBN 13: 9780471916499
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