Probability, Random Processes, and Ergodic Properties, изд. 2

Автор(ы):Robert M. Gray
06.10.2007
Год изд.:2001
Издание:2
Описание: "Василь Иваныч завалил экзамены по математике. Петька спрашивает: Что случилось". Да, вот, отвечает Василь Иваныч, спрашивают, сколько будет одна вторая плюс ноль пять. А я нутром чувствую, что литр, но обосновать не могу! Вот приблизительно об этом эта книга."
Оглавление:
Probability, Random Processes, and Ergodic Properties — обложка книги. Обложка книги.
Preface vii
  1 Probability and Random Processes [5]
    1.1 Introduction [5]
    1.2 Probability Spaces and Random Variables [5]
    1.3 Random Processes and Dynamical Systems [10]
    1.4 Distributions [12]
    1.5 Extension [17]
    1.6 Isomorphism [23]
  2 Standard alphabets [25]
    2.1 Extension of Probability Measures [25]
    2.2 Standard Spaces [26]
    2.3 Some properties of standard spaces [30]
    2.4 Simple standard spaces [33]
    2.5 Metric Spaces [35]
    2.6 Extension in Standard Spaces [40]
    2.7 The Kolmogorov Extension Theorem [41]
    2.8 Extension Without a Basis [42]
  3 Borel Spaces and Polish alphabets [49]
    3.1 Borel Spaces [49]
    3.2 Polish Spaces [52]
    3.3 Polish Schemes [58]
  4 Averages [65]
    4.1 Introduction [65]
    4.2 Discrete Measurements [65]
    4.3 Quantization [68]
    4.4 Expectation [71]
    4.5 Time Averages [81]
    4.6 Convergence of Random Variables [84]
    4.7 Stationary Averages [91]
  5 Conditional Probability and Expectation [95]
    5.1 Introduction [95]
    5.2 Measurements and Events [95]
    5.3 Restrictions of Measures [99]
    5.4 Elementary Conditional Probability [99]
    5.5 Projections [102]
    5.6 The Radon-Nikodym Theorem [105]
    5.7 Conditional Probability [108]
    5.8 Regular Conditional Probability [110]
    5.9 Conditional Expectation [113]
    5.10 Independence and Markov Chains [119]
  6 Ergodic Properties [123]
    6.1 Ergodic Properties of Dynamical Systems [123]
    6.2 Some Implications of Ergodic Properties [126]
    6.3 Asymptotically Mean Stationary Processes [131]
    6.4 Recurrence [138]
    6.5 Asymptotic Mean Expectations [142]
    6.6 Limiting Sample Averages [144]
    6.7 Ergodicity [146]
  7 Ergodic Theorems [153]
    7.1 Introduction [153]
    7.2 The Pointwise Ergodic Theorem [153]
    7.3 Block AMS Processes [158]
    7.4 The Ergodic Decomposition [160]
    7.5 The Subadditive Ergodic Theorem [164]
  8 Process Metrics and the Ergodic Decomposition [173]
    8.1 Introduction [173]
    8.2 A Metric Space of Measures [174]
    8.3 The Rho-Bar Distance [180]
    8.4 Measures on Measures [186]
    8.5 The Ergodic Decomposition Revisited [187]
    8.6 The Ergodic Decomposition of Markov Processes [190]
    8.7 Barycenters [192]
    8.8 Affine Functions of Measures [195]
    8.9 The Ergodic Decomposition of Affine Functionals [198]
Bibliography [199]
Index [204]
Формат: djvu
Размер:881888 байт
Язык:ENG
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