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☆☆☆☆☆

一個實際的隨機過程是任意一個受概率支配的過程，例子有：①看做是受孟德爾遺傳學支配的群體的發展；②受分子碰撞影響的微觀質點的布朗運動，或者是宏觀空間的星體運動；③賭場中一係列的賭博；④公路一指定點汽車的通行。

評分☆☆☆☆☆

如果係統的狀態用一個數來錶示，x(t)就是數值的，在其他情形，x(t)可以是嚮量值或者更為復雜。在本條的討論中，通常限於數值的情形。當狀態變化時，它的值確定一個時間的函數——樣本函數，支配過程的概率規律確定賦予樣本函數的各種可能性質的概率。

評分☆☆☆☆☆

原版的雖然看起來纍些，但是描述的清楚

評分☆☆☆☆☆

評分☆☆☆☆☆

原版的雖然看起來纍些，但是描述的清楚

評分☆☆☆☆☆

支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東支持京東

評分☆☆☆☆☆

一個實際的隨機過程是任意一個受概率支配的過程，例子有：①看做是受孟德爾遺傳學支配的群體的發展；②受分子碰撞影響的微觀質點的布朗運動，或者是宏觀空間的星體運動；③賭場中一係列的賭博；④公路一指定點汽車的通行。

評分☆☆☆☆☆

英文原版，新加坡的數學書一直都挺棒的。可以當做概率論的參考書目，但是有些簡略

評分☆☆☆☆☆

學習

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