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

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☆☆☆☆☆

研究隨機過程的方法多種多樣，主要可以分為兩大類：一類是概率方法，其中用到軌道性質、停時和隨機微分方程等；另一類是分析的方法，其中用到測度論、微分方程、半群理論、函數堆和希爾伯特空間等。實際研究中常常兩種方法並用。另外組閤方法和代數方法在某些特殊隨機過程的研究中也有一定作用。研究的主要內容有：多指標隨機過程、無窮質點與馬爾可夫過程、概率

評分☆☆☆☆☆

影印版，質量不錯，慢慢看吧

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。

評分☆☆☆☆☆

不錯是想要的書，比較經典

評分☆☆☆☆☆

的定義為一組隨機變量，即指定一參數集，對於其中每一參數點t指定一個隨機變量x(t)。如果迴憶起隨機變量自身就是一個函數，以ω錶示隨機變量x(t)的定義域中的一點，並以x(t，ω)錶示隨機變量在ω的值，則隨機過程就由剛纔定義的點偶(t，ω)的函數以及概率的分配完全確定。如果固定t，這個二元函數就定義一個ω的函數，即以x(t)錶示的隨機變量。如果固定ω，這個二元函數就定義一個t的函數，這是過程的樣本函數。概率

評分☆☆☆☆☆

影印版，質量不錯，慢慢看吧

評分☆☆☆☆☆

不錯不錯不錯不錯不錯

評分☆☆☆☆☆

老闆，沒有清單。。。。這個需要給一個，否則不好報銷

評分☆☆☆☆☆

不錯，內容豐富，包裝精美，推薦大傢購買。