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

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[美] 凱羅勒夫（Leonid B.Koralov） 著

圖書標籤:

• 概率論
• 隨機過程
• 高等數學
• 概率統計
• 隨機建模
• 數學建模
• 信號處理
• 通信原理
• 統計推斷
• 應用概率

齣版社： 世界圖書齣版公司

ISBN：9787510044106

版次：2

商品編碼：11124548

包裝：平裝

外文名稱：Theory of Probability and Random Processes

開本：24開

齣版時間：2012-06-01

用紙：膠版紙

頁數：353

正文語種：英文

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

評分☆☆☆☆☆

評分☆☆☆☆☆

很不錯的書，內容很詳細，很適閤自己！真心不錯！

評分☆☆☆☆☆

送不瞭就彆賣，好好一本書被弄成這樣，看著都心疼

評分☆☆☆☆☆

本書為英文原版內容不錯，對學習數學有很大幫助，是本不錯的工具書，同時有助於提高英語水平，但是發貨的包裝對書的保護嚴重不足。

評分☆☆☆☆☆

恍恍惚惚好好好好規劃和改革

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☆☆☆☆☆

666666666

評分☆☆☆☆☆

好書。簡單全麵。易有所得。oh yeah

評分☆☆☆☆☆

不錯不錯不錯不錯不錯