概率和随机_PDF下载[105MB-百度云]辛拉

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。

]

PrefaceFrequently Used NotationⅠ Measure and Integration 1 Measurable Spaces 2 Measurable Functions 3 Measures 4 Integration 5 Transforms and Indefinite Integrals 6 Kernels and Product SpacesⅡ Probability Spaces 1 Probability Spaces and Random Variables 2 Expectations 3 LP—spaces and Uniform Integrability 4 Information and Determinability 5 IndependenceⅢ 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 CentraILimitsⅣ Conditioning 1 Conditional Expectations 2 Conditional Probabilities and Distributions 3 Conditionallndependence 4 Construction of Probability Spaces 5 Spe ConstructionsⅤ 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 MartingalesⅥ 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 ProcessesⅦ 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 ProcessesⅧ 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 ExistenceⅨ 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 IntegrationNotes and CommentsBibliographyIndex