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Random ProcessesPDF|Epub|txt|kindle电子书版本网盘下载

Random Processes
  • Murray Rosenblatt 著
  • 出版社： Inc.
  • ISBN：
  • 出版时间：1962
  • 标注页数：208页
  • 文件大小：43MB
  • 文件页数：215页
  • 主题词：

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图书目录

Ⅰ．Introduction3

Ⅱ．Basic Notions for Finite and Denumerable State Models6

a．Events and Probabilities of Events6

b．Conditional Probability，Independence，and Random Variables10

c．The Binomial and Poisson distributions13

d．Expectation and Variance of Random Variables (Moments)15

e．The Weak Law of Large Numbers and the Central Limit Theorem20

f．Entropy of an Experiment29

g．Problems32

Ⅲ．Markov Chains36

a．The Markov Assumption36

b．Matrices with Non-negative Elements (Approach of Perron-Frobenius)44

c．Limit Properties for Markov Chains52

d．Functions of a Markov Chain59

e．Problems64

Ⅳ．Probability Spaces with an Infinite Number of Sample Points68

a．Discussion of Basic Concepts68

b．Distribution Functions and Their Transforms80

c．Derivatives of Measures and Conditional Probabilities86

d．Random Processes91

e．Problems96

Ⅴ．Stationary Processes100

a．Definition100

b．The Ergodic Theorem and Stationary Processes103

c．Convergence of Conditional Probabilities112

d．Macmillan＇s Theorem114

e．Problems118

Ⅵ．Markov Processes120

a．Definition120

b．Jump Processes with Continuous Time124

c．Diffusion Processes133

d．A Refined Model of Brownian Motion137

e．Pathological Jump Processes141

f．Problems146

Ⅶ．Weakly Stationary Processes and Random Harmonic Analysis149

a．Definition149

b．Harmonic Representation of a Stationary Process and Random Integrals153

c．The Linear Prediction Problem and Autoregressive Schemes160

d．Spectral Estimates for Normal Processes169

e．Problems178

Ⅷ．Additional Topics182

a．A Zero-One Law182

b．Markov Chains and Independent Random Variables183

c．A representation for a Class of Random Processes185

d．A Uniform Mixing Condition and Narrow Band-Pass Filtering195

e．Problems201

References203

Index207

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