Selfsimilar processes:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Princeton [u.a.]
Princeton Univ. Press
2002
|
| Schriftenreihe: | Princeton series in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 111 S. graph. Darst. |
| ISBN: | 0691096279 |
Internformat
MARC
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| 245 | 1 | 0 | |a Selfsimilar processes |c Paul Embrechts and Makoto Maejima |
| 264 | 1 | |a Princeton [u.a.] |b Princeton Univ. Press |c 2002 | |
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Introduction 1
1.1 Definition of Selfsimilarity 1
1.2 Brownian Motion 4
1.3 Fractional Brownian Motion 5
1.4 Stable Levy Processes 9
1.5 Lamperti Transformation 11
Chapter 2. Some Historical Background 13
2.1 Fundamental Limit Theorem 13
2.2 Fixed Points of Renormalization Groups 15
2.3 Limit Theorems (I) 16
Chapter 3. Selfsimilar Processes with Stationary Increments 19
3.1 Simple Properties 19
3.2 Long Range Dependence (I) 21
3.3 Selfsimilar Processes with Finite Variances 22
3.4 Limit Theorems (II) 24
3.5 Stable Processes 27
3.6 Selfsimilar Processes with Infinite Variance 29
3.7 Long Range Dependence (II) 34
3.8 Limit Theorems (III) 37
Chapter 4. Fractional Brownian Motion 43
4.1 Sample Path Properties 43
4.2 Fractional Brownian Motion for H ¥* 1/2 is not a Semimartingale 45
4.3 Stochastic Integrals with respect to Fractional Brownian Motion 47
4.4 Selected Topics on Fractional Brownian Motion 51
4.4.1 Distribution of the Maximum of Fractional Brownian Motion 51
4.4.2 Occupation Time of Fractional Brownian Motion 52
4.4.3 Multiple Points of Trajectories of Fractional Brownian Motion 53
4.4.4 Large Increments of Fractional Brownian Motion 54
VJjj CONTENTS
Chapter 5. Selfsimilar Processes with Independent Increments 57
5.1 K. Sato s Theorem 57
5.2 Getoor s Example 60
5.3 Kawazu s Example 61
5.4 A Gaussian Selfsimilar Process with Independent Increments 62
Chapter 6. Sample Path Properties of Selfsimilar Stable Processes with Stationary
Increments 63
6.1 Classification 63
6.2 Local Time and Nowhere Differentiability 64
Chapter 7. Simulation of Selfsimilar Processes 67
7.1 Some References 67
7.2 Simulation of Stochastic Processes 67
7.3 Simulating Levy Jump Processes 69
7.4 Simulating Fractional Brownian Motion 71
7.5 Simulating General Selfsimilar Processes 77
Chapter 8. Statistical Estimation 81
8.1 Heuristic Approaches 81
8.1.1 The R/S Statistic 82
8.1.2 The Correlogram 85
8.1.3 Least Squares Regression in the Spectral Domain 87
8.2 Maximum Likelihood Methods 87
8.3 Further Techniques 90
Chapter 9. Extensions 93
9.1 Operator Selfsimilar Processes 93
9.2 Semi Selfsimilar Processes 95
References 101
Index 109
|
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| id | DE-604.BV014313755 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:01:32Z |
| institution | BVB |
| isbn | 0691096279 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009819417 |
| oclc_num | 248316027 |
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| physical | X, 111 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series2 | Princeton series in applied mathematics |
| spelling | Embrechts, Paul 1953- Verfasser (DE-588)115254447 aut Selfsimilar processes Paul Embrechts and Makoto Maejima Princeton [u.a.] Princeton Univ. Press 2002 X, 111 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Princeton series in applied mathematics Stochastischer Prozess - Selbstähnlichkeit Selbstähnlichkeit (DE-588)4286650-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 s Selbstähnlichkeit (DE-588)4286650-9 s DE-604 Maejima, Makoto Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009819417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Embrechts, Paul 1953- Maejima, Makoto Selfsimilar processes Stochastischer Prozess - Selbstähnlichkeit Selbstähnlichkeit (DE-588)4286650-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4286650-9 (DE-588)4057630-9 |
| title | Selfsimilar processes |
| title_auth | Selfsimilar processes |
| title_exact_search | Selfsimilar processes |
| title_full | Selfsimilar processes Paul Embrechts and Makoto Maejima |
| title_fullStr | Selfsimilar processes Paul Embrechts and Makoto Maejima |
| title_full_unstemmed | Selfsimilar processes Paul Embrechts and Makoto Maejima |
| title_short | Selfsimilar processes |
| title_sort | selfsimilar processes |
| topic | Stochastischer Prozess - Selbstähnlichkeit Selbstähnlichkeit (DE-588)4286650-9 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastischer Prozess - Selbstähnlichkeit Selbstähnlichkeit Stochastischer Prozess |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009819417&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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