经典英文数学教材系列：概率和鞅 [Probability with Martingales] 下载 mobi epub pdf 电子书 2025

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　　《概率和鞅》的最大特点是将概率论讲述的清新易懂，通过有选择性的讲述，恰到好处的给出了理解基础部分的关键，一些测度论的重要观点都在《概率和鞅》的主体部分给出了很好的表述。附录中给出了有关测度论的完整证明。

内容简介

　　《概率和鞅》是一部现代概率本科教程，内容生动，叙述严格，主要以离散时间的Doob鞅理论为框架，证明了Kolmogorov强大数定理和三级数理论以及通过运用特征函数的中心极限定理这些重要的结果。概率论作为一门应用学科已经广泛的应用于物理、工程、生物、经济以及社会科学等众多领域。

内页插图

目录

Preface-please read!
A Question of Terminology
A Guide to Notation
Chapter 0 A Branching-Process Example
PAPR A： FOUNDATIONS
Chapter 1 Measure Spaces
Chapter 2 Events
Chapter 3 Random Variables
Chapter 4 Independence
Chapter 5 Integration
Chapter 6 Expectation
Chapter 7 An Easy Strong Law
Chapter 8 Product Measure

PART B： MARTINGALE THEORY
Chapter 9 Conditional Expectation
Chapter 10 Martingales
Chapter 11 The Convergence Theorem
Chapter 12 Martingales Bounded in
Chapter 13 Uniform Integrability
Chapter 14 UI Martingales
Chapter 15 Applications

PART C CHARACTERISTIC FUNCTIONS
Chapter 16 Basic Properties of CFs
Chapter 17 Weak Convergence
Chapter 18 The Central Limit Theorem
APPENDICES
Chapter A1：Appendix to Chapter 1
Chapter A3：Appendix to Chapter 3
Chapter A4：Appendix to Chapter 4
Chapter A5：Appendix to Chapter 5
Chapter A9：Appendix to Chapter 9
Chapter A13：Appendix to Chapter 13
Chapter A14：Appendix to Chapter 14
Chapter A18：Appendix to Chapter 16
Chapter E： Exercises
References
Index

前言/序言

　　The most important chapter in this book is Chapter E： Ezercises. I have left the interesting things for you to do. You can start now on the EG exercises， but see More about　exercises later in this Preface.
　　The book， which is essentially the set of lecture notes for a third-year undergraduate course at Cambridge， is as lively an introduction as I can manage to the rigorous theory of　probability. Since much of the book is devoted to martingales， it is bound to become very lively： look at those Exercises on Chapter 10! But， of course， there is that initial plod through the measure-theoretic foundations. It must be said however that measure theory， that most arid of subjects when done for its own sake， becomes amazingly more alive when used in probability， not only because it is then applied， but also because it is immensely enriched.

经典英文数学教材系列：概率和鞅 [Probability with Martingales] 下载 mobi epub pdf txt 电子书 格式

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统计中有时也用n很大的时候的Fn(A)值当概率的近似值。

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学好数学很重要，数学是理工科的基础

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写的很紧凑

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如前人做过的掷硬币的试验(P.44下面表)

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包装很好 全新值得购买

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