An Introduction To Stochastic Processes With Special Reference To Methods and ApplicationPDF电子书下载

Chapter 1．GENERAL INTRODUCTION 1

1．1 Preliminary remarks 1

1．2 Elements of probability theory 2

1．21 Distribution functions and their properties 4

1．3 Theoretical classification and specification of stochastic processes 9

1．31 The characteristic functional 13

Chapter 2．RANDOM SEQUENCES 15

2．1 The random walk 15

2．11 Renewals 20

2．2 Markov chains 24

2．21 Classification by asymptotic behaviour 30

2．22 Nearest neighbour systems 34

2．3 Multiplicative chains 39

Chapter 3．PROCESSES IN CONTINUOUS TIME 45

3．1 The additive process 45

3．2 Markov chains 50

3．3 Recurrence and passage times for renewal processes 56

3．31 Ergodic properties 64

3．32 Alternative method for Markov chains 67

3．4 Multiplicative chains 69

3．41 The effect of immigration 76

3．42 Point processes 78

3．5 General equations for Markov processes 83

Chapter 4．MISCELLANEOUS STATISTICAL APPLICATIONS 89

4．1 Some applications of the random walk or additive process 89

4．2 Simple renewal as a Markov process 96

4．21 Queues 98

4．3 Population growth as a multiplicative process 106

4．31 Growth and mutation in bacterial populations 113

4．32 Population genetics 120

4．4 Epidemic models 124

Chapter 5．LIMITING STOCHASTIC OPERATIONS 135

5．1 Stochastic convergence 135

5．11 Stochastic differentiation and integration 139

5．2 Stochastic linear difference and differential equations 144

5．21 Relations between direct stochastic equations and distribution equations 152

Chapter 6．STATIONARY PROCESSES 159

6．1 Processes stationary to the second order 159

6．11 The spectral function 161

6．12 Stationary point processes and covariance densities 166

6．2 Generalized harmonic analysis 168

6．21 The ergodic property 171

6．3 Processes with continuous spectra 173

6．31 Further examples of stationary processes 176

6．4 Complete stationarity 179

6．41 Recurrence times for completely stationary processes 182

6．5 Multivariate and multidimensional stationary processes 188

6．51 Isotropy and other special conditions 192

Chapter 7．PREDICTION AND COMMUNICATION THEORY 198

7．1 Linear prediction for stationary processes 198

7．11 Further associated problems 203

7．2 Theory of communication 208

Chapter 8．THE STATISTICAL ANALYSIS OF STOCHASTIC PROCESSES 221

8．1 Principles of statistical inference 221

8．11 Application to stochastic processes 226

8．2 The analysis of probability chains 228

8．21 Goodness of fit of marginal frequency distributions 238

8．3 Estimation problems 240

Chapter 9．CORRELATION ANALYSIS OF TIME-SERIES 253

9．1 Correlation and regression analysis of stationary sequences 253

9．11 Goodness of fit tests 259

9．12 Time-series specified for continuous time 265

9．13 Numerical examples 269

9．2 Harmonic(periodogram)analysis 274

9．21 Further notes and problems related to the spectrum 284

9．3 Multivariate autoregressive series 288

Bibliography 295

Glossary of stochastic processes 307

Index 308