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內容簡介

This book is primarily based on a one-year course that has been taught for a number of years at Princeton University to advanced undergraduate and graduate students. During the last year a similar course has also been taught at the University of Maryland.
We would like to express our thanks to Ms. Sophie Lucas and Prof. Rafael Herrera who read the manuscript and suggested many corrections. We are particularly grateful to Prof. Boris Gurevich for making many important sug-gestions on both the mathematical content and style.
While writing this book， L. Koralov was supported by a National Sci-ence Foundation grant （DMS-0405152）. Y. Sinai was supported by a National Science Foundation grant （DMS-0600996）.

內頁插圖

目錄

Part Ⅰ Probability Theory
1 Random Variables and Their Distributions
1.1 Spaces of Elementary Outcomes， a-Algebras， and Measures
1.2 Expectation and Variance of Random Variables on a Discrete Probability Space
1.3 Probability of a Union of Events
1.4 Equivalent Formulations of a-Additivity， Borel a-Algebras and Measurability
1.5 Distribution Functions and Densities
1.6 Problems
2 Sequences of Independent Trials
2.1 Law of Large Numbers and Applications
2.2 de Moivre-Laplace Limit Theorem and Applications
2.3 Poisson Limit Theorem.
2.4 Problems
3 Lebesgue Integral and Mathematical Expectation
3.1 Definition of the Lebesgue Integral
3.2 Induced Measures and Distribution Functions
3.3 Types of Measures and Distribution Functions
3.4 Remarks on the Construction of the Lebesgue Measure
3.5 Convergence of Functions， Their Integrals， and the Fubini Theorem
3.6 Signed Measures and the R，adon-Nikodym Theorem
3.7 Lp Spaces
3.8 Monte Carlo Method
3.9 Problems
4 Conditional Probabilities and Independence
4.1 Conditional Probabilities
4.2 Independence of Events， Algebras， and Random Variables
4.3
4.4 Problems
5 Markov Chains with a Finite Number of States
5.1 Stochastic Matrices
5.2 Markov Chains
5.3 Ergodic and Non-Ergodic Markov Chains
5.4 Law of Large Numbers and the Entropy of a Markov Chain
5.5 Products of Positive Matrices
5.6 General Markov Chains and the Doeblin Condition
5.7 Problems
6 Random Walks on the Lattice Zd
6.1 Recurrent and Transient R，andom Walks
6.2 Random Walk on Z and the Refiection Principle
6.3 Arcsine Law
6.4 Gambler's Ruin Problem
6.5 Problems
7 Laws of Larze Numbers
7.1 Definitions， the Borel-Cantelli Lemmas， and the Kolmogorov Inequality
7.2 Kolmogorov Theorems on the Strong Law of Large Numbers
7.3 Problems
8 Weak Converaence of Measures
8.1 Defnition of Weak Convergence
8.2 Weak Convergence and Distribution Functions
8.3 Weak Compactness， Tightness， and the Prokhorov Theorem
8.4 Problems
9 Characteristic Functions
9.1 Definition and Basic Properties
9.2 Characteristic Functions and Weak Convergence
9.3 Gaussian Random Vectors
9.4 Problems
10 Limit Theorems
10.1 Central Limit Theorem， the Lindeberg Condition
10.2 Local Limit Theorem
10.3 Central Limit Theorem and Renormalization GrOUD Theorv
10.4 Probabilities of Large Deviations
……
Part Ⅱ Random Processes
Index

前言/序言

概率論和隨機過程（第2版） [Theory of Probability and Random Processes] 下載 mobi epub pdf txt 電子書

評分☆☆☆☆☆

原版的雖然看起來纍些，但是描述的清楚

評分☆☆☆☆☆

好書。簡單全麵。易有所得。oh yeah

評分☆☆☆☆☆

好書好書好書好書好書好書好書好書

評分☆☆☆☆☆

這次滿減買的 買瞭N多quant書存起來慢慢看

評分☆☆☆☆☆

Gooooooooooooooooooooooood

評分☆☆☆☆☆

這個概率論我本科的時候沒學好，現在補一補

評分☆☆☆☆☆

的定義為一組隨機變量，即指定一參數集，對於其中每一參數點t指定一個隨機變量x(t)。如果迴憶起隨機變量自身就是一個函數，以ω錶示隨機變量x(t)的定義域中的一點，並以x(t，ω)錶示隨機變量在ω的值，則隨機過程就由剛纔定義的點偶(t，ω)的函數以及概率的分配完全確定。如果固定t，這個二元函數就定義一個ω的函數，即以x(t)錶示的隨機變量。如果固定ω，這個二元函數就定義一個t的函數，這是過程的樣本函數。概率

評分☆☆☆☆☆

在每一種情形，一個隨機係統在演化，這就是說它的狀態隨著時間而改變，於是，在時間t的狀態具有偶然性，它是一個隨機變量x(t)，參數t的集通常是一個區間(連續參數的隨機過程)或一個整數集閤(離散參數的隨機過程)。然而，有些作者隻把隨機過程這個術語用於連續參數的情形。

評分☆☆☆☆☆

很好的教材，贊一個！

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