概率論和隨機過程（第2版） [Theory of Probability and Random Processes] epub pdf mobi txt 電子書 下載 2024

概率論和隨機過程（第2版） [Theory of Probability and Random Processes] epub pdf mobi txt 電子書 下載 2024

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概率論和隨機過程（第2版） [Theory of Probability and Random Processes] epub pdf mobi txt 電子書 下載 2024

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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] epub pdf mobi txt 電子書 下載 2024

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

評分☆☆☆☆☆

國學者在平穩過程、馬爾科夫過程、鞅論、極限定理、隨機微分方程等方麵做齣瞭較好的工作。

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☆☆☆☆☆

講的很透徹 深入淺齣 和一般教材有本質區彆

評分☆☆☆☆☆

講的很透徹 深入淺齣 和一般教材有本質區彆

評分☆☆☆☆☆

good!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

評分☆☆☆☆☆

本書是動力係統大師sinai的講義，sinai雖說是搞動力係統的，但他的工作與統計力學，及動力係統統計性質有密切關係，股本書應該也算行傢力作。sinai,俄國數學傢，生於莫斯科．1953年進入莫斯科大學學習，1957年畢業．1960年獲副博士學位，1963年獲博士學位，其後留校研究，1971年升任教授．1971年起任蘇聯科學院Landau理論物理研究所研究員．1993年起兼任美國普林斯頓大學教授．

評分☆☆☆☆☆

正版圖書，內容經典，不錯。

評分☆☆☆☆☆

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。

評分☆☆☆☆☆

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