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☆☆☆☆☆

剛收到書，還沒有看，希望能讀完吧，大傢的評價都還不錯。

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Sinal是統計物理學的數學問題的國際權威，特彆是對遍曆理論有突齣貢獻．他首次給齣任意保測映射的不變量摘以嚴格定義．其後證明彈子運動的遍曆性以及擬周期Schr?dinger方程的譜性質.

評分☆☆☆☆☆

數學上的隨機過程是由實際隨機過程概念引起的一種數學結構。人們研究這種過程，是因為它是實際隨機過程的數學模型，或者是因為它的內在數學意義以及它在概率論領域之外的應用。數學上的隨機過程可以簡單

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恍恍惚惚好好好好規劃和改革

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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☆☆☆☆☆

剛收到書，還沒有看，希望能讀完吧，大傢的評價都還不錯。

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和紅紅火火恍恍惚惚哈哈

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與位勢及各種特殊過程的專題討論等。中

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

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