# 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 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 Рейтинг: 70
 Открыть: Ссылка (RU)