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An Introduction To Stochastic Processes With Special Reference To Methods and ApplicationPDF|Epub|txt|kindle电子书版本网盘下载

M.S.Bartlett 著
出版社：
ISBN：
出版时间：1955
标注页数：312页
文件大小：38MB
文件页数：322页
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图书目录

Chapter 1．GENERAL INTRODUCTION1

1．1 Preliminary remarks1

1．2 Elements of probability theory2

1．21 Distribution functions and their properties4

1．3 Theoretical classification and specification of stochastic processes9

1．31 The characteristic functional13

Chapter 2．RANDOM SEQUENCES15

2．1 The random walk15

2．11 Renewals20

2．2 Markov chains24

2．21 Classification by asymptotic behaviour30

2．22 Nearest neighbour systems34

2．3 Multiplicative chains39

Chapter 3．PROCESSES IN CONTINUOUS TIME45

3．1 The additive process45

3．2 Markov chains50

3．3 Recurrence and passage times for renewal processes56

3．31 Ergodic properties64

3．32 Alternative method for Markov chains67

3．4 Multiplicative chains69

3．41 The effect of immigration76

3．42 Point processes78

3．5 General equations for Markov processes83

Chapter 4．MISCELLANEOUS STATISTICAL APPLICATIONS89

4．1 Some applications of the random walk or additive process89

4．2 Simple renewal as a Markov process96

4．21 Queues98

4．3 Population growth as a multiplicative process106

4．31 Growth and mutation in bacterial populations113

4．32 Population genetics120

4．4 Epidemic models124

Chapter 5．LIMITING STOCHASTIC OPERATIONS135

5．1 Stochastic convergence135

5．11 Stochastic differentiation and integration139

5．2 Stochastic linear difference and differential equations144

5．21 Relations between direct stochastic equations and distribution equations152

Chapter 6．STATIONARY PROCESSES159

6．1 Processes stationary to the second order159

6．11 The spectral function161

6．12 Stationary point processes and covariance densities166

6．2 Generalized harmonic analysis168

6．21 The ergodic property171

6．3 Processes with continuous spectra173

6．31 Further examples of stationary processes176

6．4 Complete stationarity179

6．41 Recurrence times for completely stationary processes182

6．5 Multivariate and multidimensional stationary processes188

6．51 Isotropy and other special conditions192

Chapter 7．PREDICTION AND COMMUNICATION THEORY198

7．1 Linear prediction for stationary processes198

7．11 Further associated problems203

7．2 Theory of communication208

Chapter 8．THE STATISTICAL ANALYSIS OF STOCHASTIC PROCESSES221

8．1 Principles of statistical inference221

8．11 Application to stochastic processes226

8．2 The analysis of probability chains228

8．21 Goodness of fit of marginal frequency distributions238

8．3 Estimation problems240

Chapter 9．CORRELATION ANALYSIS OF TIME-SERIES253

9．1 Correlation and regression analysis of stationary sequences253

9．11 Goodness of fit tests259

9．12 Time-series specified for continuous time265

9．13 Numerical examples269

9．2 Harmonic(periodogram)analysis274

9．21 Further notes and problems related to the spectrum284

9．3 Multivariate autoregressive series288

Bibliography295

Glossary of stochastic processes307

Index308