Counterexamples in probability
著者
書誌事項
Counterexamples in probability
（Wiley series in probability and mathematical statistics, . Probability and mathematical statistics）
Wiley, c1987
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注記
Bibliography: p. 293-309
Includes index
内容説明・目次
内容説明
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.
目次
- RANDOM EVENTS AND THEIR PROBABILITIES: Classes of Random Events
- Probabilities
- Independence of Random Events
- Diverse Properties of Random Events and their Probabilities
- RANDOM VARIABLES, DISTRIBUTIONS AND BASIC CHARACTERISTICS: Distribution Functions of Random Variables
- Expectations and Conditional Expectations
- Independence of Random Variables
- Characteristic and Generating Functions
- Infinitely Divisible and Stable Distributions
- Normal Distribution
- The Moment Problem
- Characterization Properties of some Probability Distributions
- Diverse Properties of Random Variables
- LIMIT THEOREMS: Various Kinds of Convergence of Sequences of Random Variables
- Laws of Large Numbers
- Weak Convergence of Probability Measures and Distributions
- Central Limit Theorem
- Diverse Limit Theorems
- STOCHASTIC PROCESSES: Basic Notation on Stochastic Processes
- Markov Processes
- Stationary Processes and some Related Topics
- Discrete-Time Martingales
- Continuous-Time Martingales
- Poisson Process and Wiener Process
- Diverse Properties of Stochastics Processes
- Index.
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