概率和随机（英文影印版）
作者：（美）辛拉（ErhanCinlar） 著
出版时间：2015年版
内容简介
This is an introduction to the modern theory of probability and stochastic processes. The aim is to enable the student to have access to the many excellent research monographs in the literature. It might be regarded as an updated version of the textbooks by Breiman, Chung, and Neveu, just to name three.
The book is based on the lecture notes for a two-semester course which I have offered for many years. The course is fairly popular and attracts grad uate students in engineering, economics, physics, and mathematics, and a few overachieving undergraduates. Most of the students had familiarity with elementary probability, but it was safer to introduce each concept carefully and in a uniform style,
As Martin Barlow put it once, mathematics attracts us because the need to memorize is minimal. So, only the more fundamental facts are labeled as theorems; they are worth memorizing. Most other results are put as propo- sitions, comments, or exercises Also put as exercises are results that can be understood only by doing the tedious work necessary. I believe in the Chinese proverb: I hear, I forget; I see, I remember; I do, I know.
I have been considerate: I do not assume that the reader will go through the book line by line from the beginning to the end. Some things are re called or re-introduced when they are needed. In each chapter or section, the essential material is put first, technical material is put toward the end. Sub-hea-dings are used to introduce the subjects and results; the reader should
have a quick overview by flipping the pages and reading the headings.
The style and coverage is geared toward.the theory of stochastic processes, but with some attention to the applications. The reader will find many in- stances where the gist of the problem is introduced in practical, everyday language, and then is made precise in mathematical form. Conversely, many a theoretical point is re-stated in heuristic terms in order to develop the intuition and to provide some experience in stochastic modeling.
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 Special 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
