Sojourns and extremes of stochastic processes:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Pacific Grove, Calif.
Wadsworth & Brooks/Cole Advanced Books & Software
1992
|
| Schriftenreihe: | The Wadsworth & Brooks Cole statistics probability series
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 300 S. |
| ISBN: | 0534139329 |
Internformat
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| 245 | 1 | 0 | |a Sojourns and extremes of stochastic processes |c Simeon M. Berman |
| 264 | 1 | |a Pacific Grove, Calif. |b Wadsworth & Brooks/Cole Advanced Books & Software |c 1992 | |
| 300 | |a XIV, 300 S. | ||
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| 490 | 0 | |a The Wadsworth & Brooks Cole statistics probability series | |
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| 650 | 4 | |a Valeurs extrêmes, Théorie des | |
| 650 | 7 | |a Valeurs extrêmes, théorie des |2 ram | |
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Datensatz im Suchindex
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| adam_text | Contents
1 Sojourn Time Distributions 1
1.0 Summary 1
1.1 An Elementary Lemma 2
1.2 Rare Sets 5
1.3 Convergence of Mixtures of Distributions 8
1.4 A First Sojourn Limit Theorem 11
1.5 Zero one Valued Stochastic Processes 14
1.6 Separation of Sojourn Times 15
1.7 A Second Sojourn Limit Theorem 17
1.8 Extreme Sojourns: Stationary Processes 20
2 Survey of the Normal Distribution 23
2.0 Summary 23
2.1 Several Dimensions 24
2.2 Conditional Distributions 27
2.3 Hermite Polynomials 28
2.4 A Partial Differential Equation 29
ix
x Contents
2.5 Special Estimates for the Bivariate Density 31
2.6 A Comparison of Two Joint Distributions 34
3 Stationary Gaussian Processes on a
Finite Interval 39
3.0 Summary 39
3.1 Gaussian Processes 40
3.2 Regular Variation 43
3.3 Sojourns of a Stationary Gaussian Process 45
3.4 Extension to Locally Stationary Processes 50
4 Processes with Stationary
Independent Increments 55
4.0 Summary 55
4.1 Basic Properties of the Process 55
I 4.2 The Sojourn Limit Theorem 57
5 Diffusion Processes 61
5.0 Summary 61
5.1 Definitions and Notation 63
5.2 Regular Oscillation 65
5.3 Stationary Density 67
5.4 Estimates of the Distribution of the Maximum 70
5.5 The Sojourn Limit Theorem 72
5.6 Identification of the Limit 78
5.7 A Canonical Transformation 81
Contents xi
5.8 Transformation of the Sojourn Integral 82
5.9 High level Sojourns 84
5.10 Sojourns Between Two Levels 88
5.11 Sojourns for a Long Time Interval 91
5.12 Appendix: Local Time 94
6 Random Walk and Birth and Death
Processes 97
6.0 Summary 97
6.1 Definitions and Notation 98
6.2 Random Walk: Preliminaries 98
6.3 The Generating Function 100
6.4 Sojourn Limit Theorems 101
6.5 Extensions to the Birth and Death Process 103
6.6 Sojourns for a Long Time Interval 107
7 Stationary Gaussian Processes on a
Long Interval 111
7.0 Summary 111
7.1 Multinomial Poisson Limit 113
7.2 Poisson Limit for Nonnegative Arrays 117
7.3 Stationary Gaussian Processes: Preliminaries 122
7.4 Extreme Sojourns for Long Times 126
8 Central Limit Theorems 139
8.0 Summary 139
xii Contents
8.1 Basic Estimates 141
8.2 Slowly Decreasing Covariances 143
8.3 The Mixing Condition r e Lx 149
8.4 Related Covariances 153
8.5 Additional Asymptotic Estimates 155
8.6 The Auxiliary Process 157
8.7 The Mixing Condition b e Lx n L2 161
8.8 A Sufficient Condition 166
8.9 Asymptotic Estimates of the Variance 167
8.10 Estimation of the Spectral Distribution Tail 171
8.11 Asymptotic Independence at Several High Levels 174
8.12 Limiting Distribution of the Estimator 177
8.13 Asymptotic Efficiency 180
9 Extremes of Gaussian Sequences and
Diffusion Processes 183
9.0 Summary 183
9.1 Classical Extreme Value Theory 185
9.2 Maximum of a Gaussian Sequence 186
9.3 Maximum with a Random Index 190
9.4 Maximum of a Diffusion Process 192
10 Maximum of a Gaussian Process 195
10.0 Summary 195
10.1 Extensions of Fernique s Inequality 197
10.2 Asymptotic Bounds 201
Contents xiii
10.3 Weak Convergence of Gaussian Processes 202
10.4 The Supremum and Sojourn Distributions 204
10.5 Tail of the Distribution of the Maximum 205
10.6 Maximum Distribution Limit 211
11 Other Gaussian Sequences and
Markov Random Fields 215
11.0 Summary 215
11.1 Auxiliary Results 216
11.2 Mixing Denned by Conditioning 217
11.3 Maximum in a Gaussian Sequence 222
11.4 Maximum in a Markov Chain 227
11.5 Stationary Random Fields 230
11.6 Markov Random Fields 234
11.7 Maximum in a Markov Field 237
12 Processes (X, f(t)) with Orthogonally
Invariant X 243
12.0 Summary 243
12.1 Orthogonally Invariant Random Vectors 245
12.2 Type I Extreme Value Domain 2 51
12.3 Asymptotic Properties of the Mapping Gn^Gm 255
12.4 Conditional Limiting Normal Distribution (Type I) 261
12.5 Multivariate Normal Limit 263
12.6 Conditional Limits (Type II) 265
12.7 Conditional Limits (Type III) 266
xiv Contents
12.8 The Class of Stochastic Processes (X,f(*)) 268
12.9 Conditional Convergence of Distributions (Type I) 272
12.10 Separation Condition (Type I) 274
12.11 Sojourn Limit Theorem (Type I) 276
12.12 Sojourn Limit Theorem (Type II) 278
12.13 Conditional Convergence of Distributions
(Type III) 279
12.14 Separation Condition (Type III) 281
12.15 Sojourn Limit Theorem (Type III) 281
12.16 Distribution of the Maximum 283
12.17 Asymptotics of the Maximum (Type I) 285
12.18 Asymptotics of the Maximum (Type II) 286
12.19 Asymptotics of the Maximum (Type III) 286
Bibliography 289
|
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| discipline | Informatik Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV005530611 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:31:11Z |
| institution | BVB |
| isbn | 0534139329 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003466366 |
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| physical | XIV, 300 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Wadsworth & Brooks/Cole Advanced Books & Software |
| record_format | marc |
| series2 | The Wadsworth & Brooks Cole statistics probability series |
| spelling | Berman, Simeon M. Verfasser aut Sojourns and extremes of stochastic processes Simeon M. Berman Pacific Grove, Calif. Wadsworth & Brooks/Cole Advanced Books & Software 1992 XIV, 300 S. txt rdacontent n rdamedia nc rdacarrier The Wadsworth & Brooks Cole statistics probability series Processus stochastiques Processus stochastiques ram Valeurs extrêmes, Théorie des Valeurs extrêmes, théorie des ram Extreme value theory Stochastic processes Extremwertstatistik (DE-588)4153429-3 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Extremwertstatistik (DE-588)4153429-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003466366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Berman, Simeon M. Sojourns and extremes of stochastic processes Processus stochastiques Processus stochastiques ram Valeurs extrêmes, Théorie des Valeurs extrêmes, théorie des ram Extreme value theory Stochastic processes Extremwertstatistik (DE-588)4153429-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4153429-3 (DE-588)4057630-9 |
| title | Sojourns and extremes of stochastic processes |
| title_auth | Sojourns and extremes of stochastic processes |
| title_exact_search | Sojourns and extremes of stochastic processes |
| title_full | Sojourns and extremes of stochastic processes Simeon M. Berman |
| title_fullStr | Sojourns and extremes of stochastic processes Simeon M. Berman |
| title_full_unstemmed | Sojourns and extremes of stochastic processes Simeon M. Berman |
| title_short | Sojourns and extremes of stochastic processes |
| title_sort | sojourns and extremes of stochastic processes |
| topic | Processus stochastiques Processus stochastiques ram Valeurs extrêmes, Théorie des Valeurs extrêmes, théorie des ram Extreme value theory Stochastic processes Extremwertstatistik (DE-588)4153429-3 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Processus stochastiques Valeurs extrêmes, Théorie des Valeurs extrêmes, théorie des Extreme value theory Stochastic processes Extremwertstatistik Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003466366&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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