Statistical inference for stochastic processes:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
Acad. Press
1980
|
| Series: | Probability and mathematical statistics
|
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001411463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Physical Description: | XIV, 435 S. graph. Darst. |
| ISBN: | 0120802503 |
Staff View
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| 100 | 1 | |a Basawa, Ishwar V. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Statistical inference for stochastic processes |c Ishwar V. Basawa and B. L. S. Prakasa Rao |
| 264 | 1 | |a London [u.a.] |b Acad. Press |c 1980 | |
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Record in the Search Index
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| adam_text | Contents
Preface xi
List of Notation xiii
Chapter 0 Introductory Examples of Stochastic Models
Example 1. A Random Walk Model for Neuron Firing 1
Example 2. Chain Binomial Models in Epidemiology 2
Example 3. A Population Growth Model 3
Example 4. A Spatial Model for Plant Ecology 4
Example 5. A Cluster Process for Population Settlements 4
Example 6. A Model in Population Genetics 5
Example 7. A Storage Model 5
Example 8. A Compound Poisson Model for Insurance Risk 6
Example 9. System Reliability Models 6
Example 10. A Model for Cell Kinetics 6
Example 11. Queueing Models for Telephone Calls 7
Example 12. Clustering Splitting Model for Animal Behaviour 8
Example 13. Prediction of Economic Time Series 8
Example 14. Signal Estimation 9
Bibliographical Notes 9
vi Contents
PART I SPECIAL MODELS
Chapter 1 Basic Principles and Methods of Statistical Inference
1. Introduction 10
2. The Likelihood Function and Sufficient Statistics 10
3. Frequency Approach 12
4. The Bayesian Approach 13
5. Asymptotic Inference 14
6. Nonparametric Methods 18
7. Sequential Methods 19
Bibliographical Notes 19
Chapter 2 Branching Processes
1. Introduction 20
2. The Galton Watson Process 20
3. The Markov Branching Process 29
Bibliographical Notes 32
Complements 33
Chapter 3 Simple Linear Models
1. Introduction 35
2. Prediction 36
3. Filtering Problem 38
4. Parameter Estimation 41
5. Further Topics 47
Bibliographical Notes 49
Complements 50
Chapter 4 Discrete Markov Chains
1. Introduction 52
2. Finite Markov Chains 52
3. A Macro Model (Finite State Space) 72
4. Grouped Markov Chains (Finite State Space) 74
5. Countable State Space 77
Bibliographical Notes 79
Complements 79
Contents vii
Chapter 5 Markov Chains in Continuous Time
1. Introduction 81
2. Finite Markov Chains 81
3. Queueing Models 83
4. Pure Birth Process 86
5. The Birth and Death Process 90
Bibliographical Notes 95
Complements 95
Chapter 6 Simple Point Processes
1. Introduction 98
2. Homogeneous Poisson Process 98
3. Non homogeneous Poisson Process 102
4. Compound Poisson Process 105
5. Further Topics 109
Bibliographical Notes 117
Complements 117
PART II GENERAL THEORY
Chapter 7 Large Sample Theory for Discrete Parameter Stochastic
Processes
1. Introduction 119
2. Estimation 119
3. Efficient Tests of Simple Hypotheses 137
4. Large Sample Tests 139
5. Optimal Asymptotic Tests of Composite Hypotheses 147
6. Further Topics 160
Bibliographical Notes 161
Complements 162
Chapter 8 Large Sample Theory for Continuous Parameter Stochastic
Processes
1. Introduction 166
2. Observable Coordinates 166
3. The General Problem 168
viii Contents
4. Testing Hypotheses 170
5. Estimation 181
6. Estimating the Infinitesimal Generator for a Continuous Time
Finite State Markov Process 190
7. Further Topics 198
Bibliographical Notes 198
Complements 199
Chapter 9 Diffusion Processes
1. Introduction 201
2. Diffusion Processes 203
3. Absolute Continuity of Measures for Diffusion Processes 205
4. Parameter Estimation in a Linear Stochastic Differential
Equation 210
5. Asymptotic Likelihood Theory for Multidimensional
Diffusion Processes 218
6. Hypotheses Testing for Parameters of Diffusion Processes 228
7. Sequential Estimation of the Parameters of a Diffusion Process 233
8. Sequential Test for Diffusion Processes 238
9. Bayes Estimation for Diffusion Processes 241
10. Further Topics 247
Bibliographical Notes 250
Complements 250
PART III FURTHER APPROACHES
Chapter 10 Bayesian Inference for Stochastic Processes
1. Introduction 255
2. Preliminaries 256
3. The Bernstein Von Mises Theorem 257
4. Asymptotic Behaviour of Bayes Estimators 264
5. Bayesian Testing 279
6. Further Topics 284
7. Proof of Tightness of Processes 286
Bibliographical Notes 289
Complements 289
Contents jx
Chapter 11 Nonparametric Inference for Stochastic Processes
1. Introduction 294
2. Nonparametric Estimation for Stochastic Processes 294
3. Nonparametric Tests for Stochastic Processes 324
4. Further Topics 338
Bibliographical Notes 340
Complements 340
Chapter 12 Sequential Inference for Stochastic Processes
1. Introduction 343
2. Sequential Estimation for Stochastic Processes 344
3. Sequential Tests of Hypotheses for Stochastic Processes 356
4. Sequential Tests for the Drift of Wiener Process 373
5. Further Topics 379
Bibliographical Notes 380
Complements 380
Appendix 1 Martingales
1. Martingales and Limit Theorems 383
2. A Random Central Limit Theorem for Martingales 388
3. Embedding Submartingales in Wiener Process with Drift 391
4. Structure of Continuous Parameter Martingales 393
Appendix 2 Stochastic Differential Equations
1. Stochastic Integrals 396
2. Central Limit Theorem for Vector valued Stochastic Integrals 405
3. Stochastic Differential Equations 408
Appendix 3 Proof of Sudakov s Lemma (Theorem 2.3) of Chapter 12 411
Appendix 4 Generalized Functions and Generalized Stochastic
Processes 413
References 415
Index 433
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| author | Basawa, Ishwar V. Prakasa Rao, Bhagavatula L. S. 1942- |
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| id | DE-604.BV002151351 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T07:46:47Z |
| institution | BVB |
| isbn | 0120802503 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001411463 |
| oclc_num | 263558312 |
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| physical | XIV, 435 S. graph. Darst. |
| publishDate | 1980 |
| publishDateSearch | 1980 |
| publishDateSort | 1980 |
| publisher | Acad. Press |
| record_format | marc |
| series2 | Probability and mathematical statistics |
| spellingShingle | Basawa, Ishwar V. Prakasa Rao, Bhagavatula L. S. 1942- Statistical inference for stochastic processes Processus stochastiques Statistiek gtt Statistique mathématique Stochastische modellen gtt Statistik Mathematical statistics Stochastic processes Statistische Schlussweise (DE-588)4182963-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4182963-3 (DE-588)4057630-9 |
| title | Statistical inference for stochastic processes |
| title_auth | Statistical inference for stochastic processes |
| title_exact_search | Statistical inference for stochastic processes |
| title_full | Statistical inference for stochastic processes Ishwar V. Basawa and B. L. S. Prakasa Rao |
| title_fullStr | Statistical inference for stochastic processes Ishwar V. Basawa and B. L. S. Prakasa Rao |
| title_full_unstemmed | Statistical inference for stochastic processes Ishwar V. Basawa and B. L. S. Prakasa Rao |
| title_short | Statistical inference for stochastic processes |
| title_sort | statistical inference for stochastic processes |
| topic | Processus stochastiques Statistiek gtt Statistique mathématique Stochastische modellen gtt Statistik Mathematical statistics Stochastic processes Statistische Schlussweise (DE-588)4182963-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Processus stochastiques Statistiek Statistique mathématique Stochastische modellen Statistik Mathematical statistics Stochastic processes Statistische Schlussweise Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001411463&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT basawaishwarv statisticalinferenceforstochasticprocesses AT prakasaraobhagavatulals statisticalinferenceforstochasticprocesses |
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