Fractional fields and applications:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Mathématiques et applications
73 |
| Subjects: | |
| Online Access: | BTU01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783642367380 9783642367397 |
| DOI: | 10.1007/978-3-642-36739-7 |
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Record in the Search Index
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|---|---|
| adam_text | FRACTIONAL FIELDS AND APPLICATIONS
/ COHEN, SERGE
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
FOREWORD
CONTENTS
INTRODUCTION
PRELIMINARIES
SELF-SIMILARITY
ASYMPTOTIC SELF-SIMILARITY
STATISTICS
SIMULATIONS
A APPENDIX
B APPENDIX
REFERENCES
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
FRACTIONAL FIELDS AND APPLICATIONS
/ COHEN, SERGE
: 2013
ABSTRACT / INHALTSTEXT
THIS BOOK FOCUSES MAINLY ON FRACTIONAL BROWNIAN FIELDS AND THEIR
EXTENSIONS. IT HAS BEEN USED TO TEACH GRADUATE STUDENTS AT GRENOBLE AND
TOULOUSE S UNIVERSITIES. IT IS AS SELF-CONTAINED AS POSSIBLE AND
CONTAINS NUMEROUS EXERCISES, WITH SOLUTIONS IN AN APPENDIX. AFTER A
FOREWORD BY STEPHANE JAFFARD, A LONG FIRST CHAPTER IS DEVOTED TO
CLASSICAL RESULTS FROM STOCHASTIC FIELDS AND FRACTAL ANALYSIS. A CENTRAL
NOTION THROUGHOUT THIS BOOK IS SELF-SIMILARITY, WHICH IS DEALT WITH IN A
SECOND CHAPTER WITH A PARTICULAR EMPHASIS ON THE CELEBRATED GAUSSIAN
SELF-SIMILAR FIELDS, CALLED FRACTIONAL BROWNIAN FIELDS AFTER MANDELBROT
AND VAN NESS S SEMINAL PAPER. FUNDAMENTAL PROPERTIES OF FRACTIONAL
BROWNIAN FIELDS ARE THEN STATED AND PROVED. THE SECOND CENTRAL NOTION OF
THIS BOOK IS THE SO-CALLED LOCAL ASYMPTOTIC SELF-SIMILARITY (IN SHORT
LASS), WHICH IS A LOCAL VERSION OF SELF-SIMILARITY, DEFINED IN THE THIRD
CHAPTER. A LENGTHY STUDY IS DEVOTED TO LASS FIELDS WITH FINITE VARIANCE.
AMONG THESE LASS FIELDS, WE FIND BOTH GAUSSIAN FIELDS AND NON-GAUSSIAN
FIELDS, CALLED LEVY FIELDS. THE LEVY FIELDS CAN BE VIEWED AS BRIDGES
BETWEEN FRACTIONAL BROWNIAN FIELDS AND STABLE SELF-SIMILAR FIELDS. A
FURTHER KEY ISSUE CONCERNS THE IDENTIFICATION OF FRACTIONAL PARAMETERS.
THIS IS THE RAISON D ETRE OF THE STATISTICS CHAPTER, WHERE GENERALIZED
QUADRATIC VARIATIONS METHODS ARE MAINLY USED FOR ESTIMATING FRACTIONAL
PARAMETERS. LAST BUT NOT LEAST, THE SIMULATION IS ADDRESSED IN THE LAST
CHAPTER. UNLIKE THE PREVIOUS ISSUES, THE SIMULATION OF FRACTIONAL FIELDS
IS STILL AN AREA OF ONGOING RESEARCH. THE ALGORITHMS PRESENTED IN THIS
CHAPTER ARE EFFICIENT BUT DO NOT CLAIM TO CLOSE THE DEBATE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Cohen, Serge 1964- Istas, Jacques 1966- |
| author_GND | (DE-588)1028324499 (DE-588)122197356 |
| author_facet | Cohen, Serge 1964- Istas, Jacques 1966- |
| author_role | aut aut |
| author_sort | Cohen, Serge 1964- |
| author_variant | s c sc j i ji |
| building | Verbundindex |
| bvnumber | BV041083304 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)852532528 (DE-599)DNB1035284758 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-36739-7 |
| format | Electronic eBook |
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| spelling | Cohen, Serge 1964- Verfasser (DE-588)1028324499 aut Fractional fields and applications Serge Cohen ; Jacques Istas Berlin [u.a.] Springer 2013 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier Mathématiques et applications 73 Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Multifraktal (DE-588)4808941-2 gnd rswk-swf Selbstähnlichkeit (DE-588)4286650-9 gnd rswk-swf Zufälliges Feld (DE-588)4191094-1 s Multifraktal (DE-588)4808941-2 s Selbstähnlichkeit (DE-588)4286650-9 s DE-604 Istas, Jacques 1966- Verfasser (DE-588)122197356 aut Mathématiques et applications 73 (DE-604)BV035421256 73 https://doi.org/10.1007/978-3-642-36739-7 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026060042&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026060042&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Cohen, Serge 1964- Istas, Jacques 1966- Fractional fields and applications Mathématiques et applications Zufälliges Feld (DE-588)4191094-1 gnd Multifraktal (DE-588)4808941-2 gnd Selbstähnlichkeit (DE-588)4286650-9 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4808941-2 (DE-588)4286650-9 |
| title | Fractional fields and applications |
| title_auth | Fractional fields and applications |
| title_exact_search | Fractional fields and applications |
| title_full | Fractional fields and applications Serge Cohen ; Jacques Istas |
| title_fullStr | Fractional fields and applications Serge Cohen ; Jacques Istas |
| title_full_unstemmed | Fractional fields and applications Serge Cohen ; Jacques Istas |
| title_short | Fractional fields and applications |
| title_sort | fractional fields and applications |
| topic | Zufälliges Feld (DE-588)4191094-1 gnd Multifraktal (DE-588)4808941-2 gnd Selbstähnlichkeit (DE-588)4286650-9 gnd |
| topic_facet | Zufälliges Feld Multifraktal Selbstähnlichkeit |
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