Exponential families of stochastic processes:
This book provides a comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors, two of the leading experts in the field, and several other researchers. The theory is ap...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1997
|
| Schriftenreihe: | Springer series in statistics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | This book provides a comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors, two of the leading experts in the field, and several other researchers. The theory is applied to a broad spectrum of examples. The statistical concepts are explained carefully so that probabilists with only a basic background in statistics can use the book to get into statistical inference for stochastic processes. Exercises are included to make the book useful for an advanced graduate course. |
| Beschreibung: | Literaturverz. S. 303 - 316 |
| Beschreibung: | X, 322 S. |
| ISBN: | 038794981X |
Internformat
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| 100 | 1 | |a Küchler, Uwe |d 1944- |e Verfasser |0 (DE-588)134302761 |4 aut | |
| 245 | 1 | 0 | |a Exponential families of stochastic processes |c Uwe Küchler ; Michael Sørensen |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1997 | |
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| 490 | 0 | |a Springer series in statistics | |
| 500 | |a Literaturverz. S. 303 - 316 | ||
| 520 | 3 | |a This book provides a comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors, two of the leading experts in the field, and several other researchers. The theory is applied to a broad spectrum of examples. The statistical concepts are explained carefully so that probabilists with only a basic background in statistics can use the book to get into statistical inference for stochastic processes. Exercises are included to make the book useful for an advanced graduate course. | |
| 650 | 7 | |a Analyse stochastique |2 ram | |
| 650 | 4 | |a Familles exponentielles (Statistique) | |
| 650 | 7 | |a Fonctions exponentielles (Statistique) |2 ram | |
| 650 | 4 | |a Processus stochastiques | |
| 650 | 7 | |a Stochastische processen |2 gtt | |
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Exponential families (Statistics) | |
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Datensatz im Suchindex
| _version_ | 1804126079310364672 |
|---|---|
| adam_text | Contents
Preface v
1 Introduction 1
2 Natural Exponential Families of Levy Processes 7
2.1 Definition and probabilistic properties 7
2.2 Maximum likelihood estimation 14
2.3 Exercises 15
2.4 Bibliographic notes 16
3 Definitions and Examples 19
3.1 Basic definitions 19
3.2 Markov processes in discrete time 22
3.3 More general discrete time models 23
3.4 Counting processes and marked counting processes .... 24
3.5 Diffusion type processes 27
3.6 Diffusion processes with jumps 29
3.7 Random fields 30
3.8 The significance of the nitration 31
3.9 Exercises 33
3.10 Bibliographic notes 34
4 First Properties 37
4.1 Exponential representations 37
viii Contents
4.2 Exponential families of stochastic processes with a
non empty kernel 39
4.3 Exercises 42
4.4 Bibliographic notes 43
5 Random Time Transformations 45
5.1 An important type of continuous time model 45
5.2 Statistical results 48
5.3 More general models 54
5.4 Inverse families 55
5.5 Discrete time models 57
5.6 Exercises 61
5.7 Bibliographic notes 62
6 Exponential Families of Markov Processes 65
6.1 Conditional exponential families 65
6.2 Markov processes 67
6.3 The structure of exponential families of Markov processes . 71
6.4 Exercises 77
6.5 Bibliographic notes 78
7 The Envelope Families 81
7.1 General theory 81
7.2 Markov processes 84
7.3 Explicit calculations 87
7.4 The Gaussian autoregression 90
7.5 The pure birth process 94
7.6 The Ornstein Uhlenbeck process 96
7.7 A goodness of fit test 98
7.8 Exercises 100
7.9 Bibliographic notes 101
8 Likelihood Theory 103
8.1 Likelihood martingales 103
8.2 Existence and uniqueness of the maximum likelihood
estimator 108
8.3 Consistency and asymptotic normality of the maximum
likelihood estimator 113
8.4 Information matrices 124
8.5 Local asymptotic mixed normality 128
8.6 Exercises 130
8.7 Bibliographic notes 133
Contents ix
9 Linear Stochastic Differential Equations with Time Delay 135
9.1 The differential equations and the maximum likelihood
estimator 135
9.2 The fundamental solution xq( ) 139
9.3 Asymptotic likelihood theory 141
9.4 The case N = 1 145
9.5 Exercises 155
9.6 Bibliographic notes 156
10 Sequential Methods 157
10.1 Preliminary results 157
10.2 Exact likelihood theory 161
10.3 Asymptotic likelihood theory 173
10.4 Comparison of sampling times 181
10.5 Moments of the stopping times 187
10.6 The sequential probability ratio test 192
10.7 Exercises 201
10.8 Bibliographic notes 203
11 The Semimartingale Approach 205
11.1 The local characteristics of a semimartingale 205
11.2 The natural exponential family generated by a
semimartingale 208
11.3 Exponential families with a time continuous likelihood
function 216
11.4 Other types of exponential families of semimartingales . . 221
11.5 General exponential families of Levy processes 225
11.6 Exponential families constructed by stochastic time
transformation 229
11.7 Likelihood theory 231
11.8 Exercises 237
11.9 Bibliographic notes 238
12 Alternative Definitions 241
12.1 Exponential marginal distributions 242
12.2 Families with a sufficient reduction 249
12.3 Exercises 262
12.4 Bibliographic Notes 265
A A Toolbox from Stochastic Calculus 267
A.I Stochastic basis 267
A.2 Local martingales and increasing processes 269
A.3 Doob Meyer decomposition 271
A.4 Semimartingales and stochastic integration 274
A.5 Stochastic differential equations 279
x Contents
A.6 Ito s formula 281
A.7 Martingale limit theorems 284
A.8 Stochastic integration with respect to random measures . 288
A.9 Local characteristics of a semimartingale 291
A. 10 A Girsanov type theorem for semimartingales 294
B Miscellaneous Results 299
B.I The fundamental identity of sequential analysis 299
B.2 A conditional Radon Nikodym derivative 301
B.3 Three lemmas 301
C References 303
D Basic Notation 317
Index 319
|
| any_adam_object | 1 |
| author | Küchler, Uwe 1944- Sørensen, Michael 1955- |
| author_GND | (DE-588)134302761 (DE-588)170408639 |
| author_facet | Küchler, Uwe 1944- Sørensen, Michael 1955- |
| author_role | aut aut |
| author_sort | Küchler, Uwe 1944- |
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| building | Verbundindex |
| bvnumber | BV011554138 |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.K83 1997 |
| callnumber-search | QA274.K83 1997 |
| callnumber-sort | QA 3274 K83 41997 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)36543425 (DE-599)BVBBV011554138 |
| dewey-full | 519.2 519.221 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 519.2 21 |
| dewey-search | 519.2 519.2 21 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011554138 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:11:45Z |
| institution | BVB |
| isbn | 038794981X |
| language | English |
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| physical | X, 322 S. |
| publishDate | 1997 |
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| spelling | Küchler, Uwe 1944- Verfasser (DE-588)134302761 aut Exponential families of stochastic processes Uwe Küchler ; Michael Sørensen New York [u.a.] Springer 1997 X, 322 S. txt rdacontent n rdamedia nc rdacarrier Springer series in statistics Literaturverz. S. 303 - 316 This book provides a comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors, two of the leading experts in the field, and several other researchers. The theory is applied to a broad spectrum of examples. The statistical concepts are explained carefully so that probabilists with only a basic background in statistics can use the book to get into statistical inference for stochastic processes. Exercises are included to make the book useful for an advanced graduate course. Analyse stochastique ram Familles exponentielles (Statistique) Fonctions exponentielles (Statistique) ram Processus stochastiques Stochastische processen gtt Stochastic processes Exponential families (Statistics) Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Exponentialfamilie (DE-588)4372302-0 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Exponentialfamilie (DE-588)4372302-0 s DE-604 Sørensen, Michael 1955- Verfasser (DE-588)170408639 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007779507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Küchler, Uwe 1944- Sørensen, Michael 1955- Exponential families of stochastic processes Analyse stochastique ram Familles exponentielles (Statistique) Fonctions exponentielles (Statistique) ram Processus stochastiques Stochastische processen gtt Stochastic processes Exponential families (Statistics) Stochastischer Prozess (DE-588)4057630-9 gnd Exponentialfamilie (DE-588)4372302-0 gnd |
| subject_GND | (DE-588)4057630-9 (DE-588)4372302-0 |
| title | Exponential families of stochastic processes |
| title_auth | Exponential families of stochastic processes |
| title_exact_search | Exponential families of stochastic processes |
| title_full | Exponential families of stochastic processes Uwe Küchler ; Michael Sørensen |
| title_fullStr | Exponential families of stochastic processes Uwe Küchler ; Michael Sørensen |
| title_full_unstemmed | Exponential families of stochastic processes Uwe Küchler ; Michael Sørensen |
| title_short | Exponential families of stochastic processes |
| title_sort | exponential families of stochastic processes |
| topic | Analyse stochastique ram Familles exponentielles (Statistique) Fonctions exponentielles (Statistique) ram Processus stochastiques Stochastische processen gtt Stochastic processes Exponential families (Statistics) Stochastischer Prozess (DE-588)4057630-9 gnd Exponentialfamilie (DE-588)4372302-0 gnd |
| topic_facet | Analyse stochastique Familles exponentielles (Statistique) Fonctions exponentielles (Statistique) Processus stochastiques Stochastische processen Stochastic processes Exponential families (Statistics) Stochastischer Prozess Exponentialfamilie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007779507&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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