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
大学図書館所蔵 全78件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
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.
「Nielsen BookData」 より