概率論和隨機過程（第2版） [Theory of Probability and Random Processes] 下載 mobi epub pdf 電子書 2025

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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）.

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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 格式

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很不錯的一本書，非常喜歡，送貨速度很快

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還沒看到呢，應該不錯吧，知識的力量

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還好還好………………

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　　 讀者對象：數學及相關專業的大學高年級學生和研究生。

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隨機過程

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他是俄國科學院院士及美國文理科學院院士，他還是倫敦數學會名譽會員．他曾榮獲Boltzmann金質奬章（1986）；Heinemann奬（1989）；Markov奬（1990）以及意大利Trieste國際理論物理中心Dirac奬章（1992）．1997年因“對統計力學中數學嚴格方法及動力係統的遍曆理論以及它們在物理學中的應用所做的基本貢獻”而獲Wolf奬.他的工作是特彆令人印象深刻的廣度。 “[西奈半島的工作除瞭其持久的影響在純數學]已經起到瞭至關重要的作用創造動力的混亂，這已經被極其重要的物理學和非綫性科學的發展在過去的三概念五年“。引用注意到壓倒性的影響西奈半島的工作，在過去的半個世紀中，包括他的250多篇研究論文，他的幾本書。他監督瞭50多個博士生，其中許多人已成為在自己的權利領域的領導者。引用的結論是，“斯蒂爾被授予終身成就奬西奈承認所有這些成就。

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