Essentials of Probability and Statistical Inference IV: Algorithmic and NonParametic Approaches
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课程名称：
Essentials of Probability and Statistical Inference IV: Algorithmic and NonParametic Approaches
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约翰霍普金斯大学
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Rafael Irizarry
生物统计学
内容简介：
Introduces the theory and application of modern, computationally-based methods for exploring and drawing inferences from data. Covers re-sampling methods, non-parametric regression, prediction, and d ...
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Statistics of Random Processes II: Applications [平装]
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& && &&&&Written by two renowned experts in the field, the books under review contain a thorough and insightful treatment of the fundamental underpinnings of various aspects of stochastic processes as well as a wide range of applications. Providing clear exposition, deep mathematical results, and superb technical representation, they are masterpieces of the subject of stochastic analysis and nonlinear filtering...These books...will become classics.& --SIAM REVIEW
基本信息& && &出版社: Springer-Verlag Berlin and Heidelberg GmbH & Co. K; Softcover reprint of hardcover 2nd ed. 年12月1日)丛书名: 平装: 417页语种：英语ISBN: X条形码: 5商品尺寸:
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Preface to the Second Edition
Introduction
1. Essentials of Probability Theory and Mathematical Statistics
　1.1 Main Concepts of Probability Theory
　1.2 Random Processes: Basic Notions
　1.3 Markov Times
　1.4 Brownian Motion Processes
　1.5 Some Notions from Mathematical Statistics
2. Martingales and Related Processes: Discrete Time
　2.1 Supermartingales and Submartingales on a Finite Time Interval
　2.2 Submartingales on an Infinite Time Interval, and the Theorem of Convergence
　2.3 Regular Martingales: Levy's Theorem
　2.4 Invariance of the Supermartingale Property for Markov Times: Riesz and Doob Decompositions
3. Martingales and Related Processes: Continuous Time
　3.1 Right Continuous Supermartingales
　3.2 Basic Inequalities, the Theorem of Convergence, and Invari-ance of the Supermartingale Property for Markov Times
　3.3 Doob-Meyer Decomposition for Supermartingales
　3.4 Some Properties of Predictable Increasing Processes
4. The Wiener Process, the Stochastic Integral over the Wiener Process, and Stochastic Differential Equations
　4.1 The Wiener Process as a Square Integrable Martingale
　4.2 Stochastic Integrals: It6 Processes
　4.3 It6's Formula
　4.4 Strong and Weak Solutions of Stochastic Differential Equations:
5. Square Integrable Martingales and Structure of the Functionals on a Wiener Process
　5.1 Doob-Meyer Decomposition for Square Integrable Martingales
　5.2 Representation of Square Integrable Martingales
　5.3 The Structure of Functionals of a Wiener Process
　5.4 Stochastic Integrals over Square Integrable Martingales
　5.5 Integral Representations of the Martingales which are Conditional Expectations and the Fubini Theorem for Stochastic Integrals
　5.6 The Structure of Functionals of Processes of the Diffusion Type
6. Nonnegative Supermartingales and Martingales and the Girsanov Theorem
　6.1 Nonnegative Supermartingales
　6.2 Nonnegative Martingales
　6.3 The Girshanov Theorem and its Generalization
7. Absolute Continuity of Measures corresponding to the It Processes and Processes of the Diffusion Type
7.1 The It5 Processes, and the Absolute Continuity of their Measures with respect to Wiener Measure
　7.2 Processes of the Diffusion Type: the Absolute Continuity of their Measures with respect to Wiener Measure
　7.3 The Structure of Processes whose Measure is Absolutely Continuous with Respect to Wiener Measure
　7.4 Representation of the It6 Processes as Processes of the Diffusion Type, Innovation Processes, and the Struc ture of Functionals on the It5 Process
　7.5 The Case of Gaussian Processes
　7.6 The Absolute Continuity of Measures of the It5 Processes with respect to Measures Corresponding to Processes of the Diffusion Type
　7.7 The Cameron-Martin Formula
　7.8 The Cramer-Wolfowitz Inequality
　7.9 An Abstract Version of the Bayes Formula
8. General Equations of Optimal Nonlinear Filtering, Interpolation and Extrapolation of Partially Observable Random Processes
　8.1 Filtering: the Main Theorem
　8.2 Filtering: Proof of the Main Theorem
　8.3 Filtering of Diffusion Markov Processes
　8.4 Equations of Optimal Nonlinear Interpolation
8.5 Equations of Optimal Nonlinear Extrapolation
9 Optimal Filtering, Interpolation and Extrapolation of Markov Processes with a Countable Number of States
10 Optimal Linear Nonstationary Filtering
Bibliography
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rmatrix 发表于
Preface to the Second Edition
Introduction
1. Essentials of Probability Theory and Mathematical St ...说好的2010年版本呢？？？
rmatrix 发表于
本论坛上有
Statistics of Random Processes I: General Theory
是双面复印版，见：
谢谢分享！
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Rick Durrett也就是Richard Durrett。
这是他的书《essentials of stochastic process》正在修改中的第二版。原书第一版是由springer出版社1999年出版的。正式的第二版估计要2013年才出。
章节目录如下。
1 Markov Chains 3
1.1 Definitions and Examples . . . . . . . . . . . . . . . 3
1.2 Multistep Transition Probabilities . . . . . . . . . . . 13
1.3 Classification of States . . . . . . . . . . . . . . . . . 18
1.4 Stationary Distributions . . . . . . . . . . . . . . . . 27
1.5 Limit Behavior . . . . . . . . . . . . . . . . . . . . . 33
1.6 Special Examples . . . . . . . . . . . . . . . . . . . . 42
1.6.1 Doubly stochastic chains . . . . . . . . . . . . 42
1.6.2 Detailed balance condition . . . . . . . . . . . 45
1.6.3 Reversibility . . . . . . . . . . . . . . . . . . . 51
1.7 Proofs of the Theorems 1.7–1.11 . . . . . . . . . . . . 53
1.8 Exit distributions . . . . . . . . . . . . . . . . . . . . 60
1.9 Exit times . . . . . . . . . . . . . . . . . . . . . . . . 68
1.10 Infinite State Spaces* . . . . . . . . . . . . . . . . . . 75
1.11 Chapter Summary . . . . . . . . . . . . . . . . . . . 83
1.12 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 87
2 Poisson Processes 107
2.1 Exponential Distribution . . . . . . . . . . . . . . . . 107
2.2 Defining the Poisson Process . . . . . . . . . . . . . . 112
2.3 Compound Poisson Processes . . . . . . . . . . . . . 120
2.4 Transformations . . . . . . . . . . . . . . . . . . . . . 123
2.4.1 Thinning . . . . . . . . . . . . . . . . . . . . . 123
2.4.2 Superposition . . . . . . . . . . . . . . . . . . 125
2.4.3 Conditioning . . . . . . . . . . . . . . . . . . 126
2.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 128
3 Renewal processes 137
3.1 Laws of large numbers . . . . . . . . . . . . . . . . . 137
3.2 Applications to Queueing Theory . . . . . . . . . . . 146
3.2.1 GI/G/1 queue . . . . . . . . . . . . . . . . . . 146
3.2.2 M/G/1 queue . . . . . . . . . . . . . . . . . . 150
3.3 Age and Residual Life . . . . . . . . . . . . . . . . . 153
3.3.1 Discrete case . . . . . . . . . . . . . . . . . . 153
3.3.2 Age . . . . . . . . . . . . . . . . . . . . . . . 155
3.3.3 General case . . . . . . . . . . . . . . . . . . . 157
3.4 Renewal equations . . . . . . . . . . . . . . . . . . . 162
3.5 Exercises . . . . . . . . . . . . . . . . . . . . . . . . 167
4 Markov Chains in
Continuous Time 171
4.1 Definitions and Examples . . . . . . . . . . . . . . . 171
4.2 Computing the Transition Probability . . . . . . . . . 179
4.3 Limiting Behavior . . . . . . . . . . . . . . . . . . . . 185
4.4 Markovian Queues . . . . . . . . . . . . . . . . . . . 192
4.5 Queueing Networks . . . . . . . . . . . . . . . . . . . 199
4.6 Closed Queueing Networks . . . . . . . . . . . . . . . 209
4.7 Exercises . . . . . . . . . . . . . . . . . . . . . . . . . 215
5 Martingales 225
5.1 Conditional Expectation . . . . . . . . . . . . . . . . 225
5.2 Examples of Martingales . . . . . . . . . . . . . . . . 228
5.3 Properties of Martingales . . . . . . . . . . . . . . . . 231
5.4 Applications . . . . . . . . . . . . . . . . . . . . . . . 235
6 Finance 239
6.1 Two simple examples . . . . . . . . . . . . . . . . . . 239
6.2 Binomial model . . . . . . . . . . . . . . . . . . . . . 245
6.3 Black-Scholes formula . . . . . . . . . . . . . . . . . . 252
A Review of Probability 259
A.1 Probabilities, Independence . . . . . . . . . . . . . . 259
A.2 Random Variables, Distributions . . . . . . . . . . . 265
A.3 Expected Value, Moments . . . . . . . . . . . . . . . 272
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This book is not recommended.. One of the most sucky books Durrett ever wrote.
多谢楼主啊！
hehe, maybe it really is
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