An introduction to stochastic processes: with special reference to methods and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
1966
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 363 S. |
Staff View
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| 100 | 1 | |a Bartlett, Maurice S. |d 1910-2002 |e Verfasser |0 (DE-588)123228247 |4 aut | |
| 245 | 1 | 0 | |a An introduction to stochastic processes |b with special reference to methods and applications |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 1966 | |
| 300 | |a XVI, 363 S. | ||
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Record in the Search Index
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| adam_text | CONTENTS
Preface to the First Edition page xi
Preface to the Second Edition page xv
Chapter 1. general introduction
§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
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 • 23 Wald s identity for Markov chains 39
2 3 Multiplicative chains ^
Chapter 3. processes in continuous time
3 1 The additive process 47
3 2 Markov chains 52
3 3 Recurrence and passage times for renewal processes 58
3 31 Ergodic properties 68
3 32 Alternative method for Markov chains 71
3 4 Multiplicative chains 73
3*41 The effect of immigration SO
3 42 Point processes 82
3 5 General equations for Markov processes 87
viii CONTENTS
Chapter 4. miscellaneous statistical applications
§4 1 Some applications of the random walk or additive
process Pa^e 95
4 2 Simple renewal as a Markov process 102
4 21 Queues 104
4 • 22 Theory of storage 113
4 3 Population growth as a multiplicative process 117
4 31 Growth and mutation in bacterial popula¬
tions 124
4 32 Population genetics 131
4 4 Epidemic models „ 135
Chapter 5. limiting stochastic operations
5 1 Stochastic convergence 147
5 11 Stochastic differentiation and integration 151
5 2 Stochastic linear difference and differential equa¬
tions 156
5 21 Relations between direct stochastic equa¬
tions and distribution equations 164
5 22 Equations for stochastic path integrals 170
Chapter 6. stationaby processes
6 1 Processes stationary to the second order 174
6 11 The spectral function 176
6 12 Stationary point processes and covariance
densities 181
6 13 The spectra of stationary point processes 183
8 2 Generalized harmonic analysis 186
6 21 The ergodic property 189
6 3 Processes with continuous spectra 191
6 31 Further examples of stationary processes 195
6 4 Complete stationarity 197
6 41 Recurrence times for completely stationary
processes 200
6 5 Multivariate and multidimensional stationary
processes 207
6 51 Isotropy and other special conditions 210
6 52 Two dimensional point and line processes 215
6 53 Stationary processes on the circle and sphere 221
CONTENTS IX
Chapter 7. prediction and communication theoby
§7 1 Linear prediction for stationary processes page 224:
7 11 Further associated problems 229
7 12 Regulation and control 234
7 • 2 Theory of information and communication 236
7 21 Communication systems 238
Chapter 8. the statistical analysis of
STOCHASTIC PBOCESSES
8 1 Principles of statistical inference 251
8 11 Application to stochastic processes 256
8 2 The analysis of probability chains 258
8 21 Goodness of fit of marginal frequency dis¬
tributions 268
8 3 Estimation problems 270
Chapter 9. cobbelation analysis of time sebies
9 1 Correlation and regression analysis of stationary
sequences 283
9 11 Goodness of fit tests 289
9 12 Time series specified for continuous time 295
9 13 Numerical examples 299
9 2 Harmonic (periodogram) analysis 304
9 21 Smoothing techniques in relation to the
mean square error 314
9 22 Further notes and problems related to the
spectrum 318
9 • 23 The spectral analysis of point processes 324
9 3 Multivariate autoregressive series 331
9 • 4 Multidimensional series 338
9 41 The analysis of multidimensional point pro¬
cesses 340
Bibliography 342
Glossary of stochastic processes 356
Index 357
|
| adam_txt |
CONTENTS
Preface to the First Edition page xi
Preface to the Second Edition page xv
Chapter 1. general introduction
§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
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 • 23 Wald's identity for Markov chains 39
2 3 Multiplicative chains ^
Chapter 3. processes in continuous time
3 1 The additive process 47
3 2 Markov chains 52
3 3 Recurrence and passage times for renewal processes 58
3 31 Ergodic properties 68
3 32 Alternative method for Markov chains 71
3 4 Multiplicative chains 73
3*41 The effect of immigration SO
3 42 Point processes 82
3 5 General equations for Markov processes 87
viii CONTENTS
Chapter 4. miscellaneous statistical applications
§4 1 Some applications of the random walk or additive
process Pa^e 95
4 2 Simple renewal as a Markov process 102
4 21 Queues 104
4 • 22 Theory of storage 113
4 3 Population growth as a multiplicative process 117
4 31 Growth and mutation in bacterial popula¬
tions 124
4 32 Population genetics 131
4 4 Epidemic models „ 135
Chapter 5. limiting stochastic operations
5 1 Stochastic convergence 147
5 11 Stochastic differentiation and integration 151
5 2 Stochastic linear difference and differential equa¬
tions 156
5 21 Relations between direct stochastic equa¬
tions and distribution equations 164
5 22 Equations for stochastic path integrals 170
Chapter 6. stationaby processes
6 1 Processes stationary to the second order 174
6 11 The spectral function 176
6 12 Stationary point processes and covariance
densities 181
6 13 The spectra of stationary point processes 183
8 2 Generalized harmonic analysis 186
6 21 The ergodic property 189
6 3 Processes with continuous spectra 191
6 31 Further examples of stationary processes 195
6 4 Complete stationarity 197
6 41 Recurrence times for completely stationary
processes 200
6 5 Multivariate and multidimensional stationary
processes 207
6 51 Isotropy and other special conditions 210
6 52 Two dimensional point and line processes 215
6 53 Stationary processes on the circle and sphere 221
CONTENTS IX
Chapter 7. prediction and communication theoby
§7 1 Linear prediction for stationary processes page 224:
7 11 Further associated problems 229
7 12 Regulation and control 234
7 • 2 Theory of information and communication 236
7 21 Communication systems 238
Chapter 8. the statistical analysis of
STOCHASTIC PBOCESSES
8 1 Principles of statistical inference 251
8 11 Application to stochastic processes 256
8 2 The analysis of probability chains 258
8 21 Goodness of fit of marginal frequency dis¬
tributions 268
8 3 Estimation problems 270
Chapter 9. cobbelation analysis of time sebies
9 1 Correlation and regression analysis of stationary
sequences 283
9 11 Goodness of fit tests 289
9 12 Time series specified for continuous time 295
9 13 Numerical examples 299
9 2 Harmonic (periodogram) analysis 304
9 21 Smoothing techniques in relation to the
mean square error 314
9 22 Further notes and problems related to the
spectrum 318
9 • 23 The spectral analysis of point processes 324
9 3 Multivariate autoregressive series 331
9 • 4 Multidimensional series 338
9 41 The analysis of multidimensional point pro¬
cesses 340
Bibliography 342
Glossary of stochastic processes 356
Index 357 |
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| author | Bartlett, Maurice S. 1910-2002 |
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| discipline | Psychologie Mathematik Wirtschaftswissenschaften |
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| edition | 2. ed. |
| format | Book |
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| index_date | 2024-07-02T16:05:48Z |
| indexdate | 2024-07-09T20:47:28Z |
| institution | BVB |
| language | English |
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| physical | XVI, 363 S. |
| publishDate | 1966 |
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| spelling | Bartlett, Maurice S. 1910-2002 Verfasser (DE-588)123228247 aut An introduction to stochastic processes with special reference to methods and applications 2. ed. Cambridge Cambridge Univ. Press 1966 XVI, 363 S. txt rdacontent n rdamedia nc rdacarrier Probabilidade (Estatistica) larpcal Processos Estocasticos larpcal Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Stochastischer Prozess (DE-588)4057630-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015137563&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bartlett, Maurice S. 1910-2002 An introduction to stochastic processes with special reference to methods and applications Probabilidade (Estatistica) larpcal Processos Estocasticos larpcal Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4151278-9 |
| title | An introduction to stochastic processes with special reference to methods and applications |
| title_auth | An introduction to stochastic processes with special reference to methods and applications |
| title_exact_search | An introduction to stochastic processes with special reference to methods and applications |
| title_exact_search_txtP | An introduction to stochastic processes with special reference to methods and applications |
| title_full | An introduction to stochastic processes with special reference to methods and applications |
| title_fullStr | An introduction to stochastic processes with special reference to methods and applications |
| title_full_unstemmed | An introduction to stochastic processes with special reference to methods and applications |
| title_short | An introduction to stochastic processes |
| title_sort | an introduction to stochastic processes with special reference to methods and applications |
| title_sub | with special reference to methods and applications |
| topic | Probabilidade (Estatistica) larpcal Processos Estocasticos larpcal Stochastische processen gtt Stochastic processes Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Probabilidade (Estatistica) Processos Estocasticos Stochastische processen Stochastic processes Stochastischer Prozess Einführung |
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