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概率和随机 内容简介
本书是一部兼顾理论和应用的，讲述概率和随机研究生教材。本书的风格仍然是这个系列的延续，注重随机过程的理论，但却非一味强调理论和抽象，也兼顾应用。书的前四章是有关概率论、度量和积分、概率空间、条件期望和经典极限定理；接下来的章节是有关鞅、泊松随机测度、levy过程、布朗运动和马尔科夫过程。重点强调了泊松随机测度，及其在调节布朗运动冲程和Levy跃迁和马尔科夫过程中的扮演的重要角色。每章末都有大量的例子和练习。
概率和随机 目录
Preface
Frequently Used Notation
Ⅰ Measure and Integration
1 Measurable Spaces
2 Measurable Functions
3 Measures
4 Integration
5 Transforms and Indefinite Integrals
6 Kernels and Product Spaces
Ⅱ Probability Spaces
1 Probability Spaces and Random Variables
2 Expectations
3 LP—spaces and Uniform Integrability
4 Information and Determinability
5 Independence
Ⅲ Convergence
1 Convergence of Real Sequences
2 Almost Sure Convergence
3 Convergence in Probability
4 Convergencein Lp
5 Weak Convergence
6 Laws ofLarge Numbers
7 Convergence ofSeries
8 CentraILimits
Ⅳ Conditioning
1 Conditional Expectations
2 Conditional Probabilities and Distributions
3 Conditionallndependence
4 Construction of Probability Spaces
5 Spe Constructions
Ⅴ Martingales and Stochastics
1 Filtrations and Stopping Times
2 Martingales
3 Martingale Transformations and Maxima
4 Martingale Convergence
5 Martingales in Continuous Time
6 Martingale Characterizations for Wiener and Poisson
7 Standard Filtrations and Modifications of Martingales
Ⅵ Poisson Random Measures
1 Random Measures
2 Poisson Random Measures
3 Transformations
4 Additive Random Measures and Levy Processes
5 Poisson Processes
6 Poisson Integrals and Self—exciting Processes
Ⅶ Levy Processes
1 Introduction
2 Stable Processes
3 Levy Processes on Standard Settings
4 Characterizations for Wiener and Poisson
5 Ito—Levy Decomposition
6 Subordination
7 Increasing Levy Processes
Ⅷ Brownian Motion
1 Introduction
2 Hitting Times and Recurrence Times
3 Hitting Times and Running Maximum
4 Wiener and its Maximum
5 Zeros，LocaITimes
6 Excursions
7 Path Properties
8 Existence
Ⅸ Markov Processes
1 Markov Property
2 Ito Diffusions
3 Jump—Diffusions
4 Markov Systems
5 Hunt Processes
6 Potentials and Excessive Functions
7 Appendix：Stochastic Integration
Notes and Comments
Bibliography
Index
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