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: |
Обложка книги.
Preface vii1 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 |
Рейтинг: | 111 |
Открыть: | Ссылка (RU) |