《An Introduction To Stochastic Processes With Special Reference To Methods and Application》求取 ⇩

Chapter 1．GENERAL INTRODUCTION1

1．1Preliminary remarks1

1．2Elements of probability theory2

1．21 Distribution functions and their properties4

1．3Theoretical classification and specification of stochastic processes9

1．31 The characteristic functional13

Chapter 2．RANDOM SEQUENCES15

2．1The random walk15

2．11 Renewals20

2．2Markov chains24

2．21 Classification by asymptotic behaviour30

2．22 Nearest neighbour systems34

2．3 Multiplicative chains39

Chapter 3．PROCESSES IN CONTINUOUS TIME45

3．1The additive process45

3．2 Markov chains50

3．3Recurrence and passage times for renewal processes56

3．31 Ergodic properties64

3．32 Alternative method for Markov chains67

3．4Multiplicative chains69

3．41 The effect of immigration76

3．42 Point processes78

3．5 General equations for Markov processes83

Chapter 4．MISCELLANEOUS STATISTICAL APPLICATIONS89

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

4．2Simple renewal as a Markov process96

4．21 Queues98

4．3Population 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

5．1Stochastic convergence135

5．11 Stochastic differentiation and integration139

5．2Stochastic linear difference and differential equations144

5．21 Relations between direct stochastic equations and distribution equations152

Chapter 6．STATIONARY PROCESSES159

6．1Processes stationary to the second order159

6．11 The spectral function161

6．12 Stationary point processes and covariance densities166

6．2Generalized harmonic analysis168

6．21 The ergodic property171

6．3Processes with continuous spectra173

6．31 Further examples of stationary processes176

6．4Complete stationarity179

6．41 Recurrence times for completely stationary processes182

6．5Multivariate and multidimensional stationary processes188

6．51 Isotropy and other special conditions192

Chapter 7．PREDICTION AND COMMUNICATION THEORY198

7．1Linear prediction for stationary processes198

7．11 Further associated problems203

7．2 Theory of communication208

Chapter 8．THE STATISTICAL ANALYSIS OF STOCHASTIC PROCESSES221

8．1Principles of statistical inference221

8．11 Application to stochastic processes226

8．2The analysis of probability chains228

8．21 Goodness of fit of marginal frequency distributions238

8．3 Estimation problems240

Chapter 9．CORRELATION ANALYSIS OF TIME-SERIES253

9．1Correlation and regression analysis of stationary sequences253

9．11 Goodness of fit tests259

9．12 Time-series specified for continuous time265

9．13 Numerical examples269

9．2Harmonic(periodogram)analysis274

9．21 Further notes and problems related to the spectrum284

9．3 Multivariate autoregressive series288

Bibliography295

Glossary of stochastic processes307

Index308