On the estimation of multiple random integrals and U-statistics
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
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| Schriftenreihe: | Lecture notes in mathematics
2079 |
| Schlagworte: | |
| Online-Zugang: | Volltext Inhaltsverzeichnis Abstract |
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| 245 | 1 | 0 | |a On the estimation of multiple random integrals and U-statistics |c Péter Major |
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Datensatz im Suchindex
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| adam_text | ON THE ESTIMATION OF MULTIPLE RANDOM INTEGRALS AND U-STATISTICS
/ MAJOR, PETER
: 2013
TABLE OF CONTENTS / INHALTSVERZEICHNIS
1 INTRODUCTION
2 MOTIVATION OF THE INVESTIGATION. DISCUSSION OF SOME PROBLEMS
3 SOME ESTIMATES ABOUT SUMS OF INDEPENDENT RANDOM VARIABLES
4 ON THE SUPREMUM OF A NICE CLASS OF PARTIAL SUMS
5 VAPNIK– CERVONENKIS CLASSES AND L2-DENSE CLASSES OF FUNCTIONS
6 THE PROOF OF THEOREMS 4.1 AND 4.2 ON THE SUPREMUM OF RANDOM SUMS
7 THE COMPLETION OF THE PROOF OF THEOREM 4.1
8 FORMULATION OF THE MAIN RESULTS OF THIS WORK
9 SOME RESULTS ABOUT U-STATISTICS
10 MULTIPLEWIENER–ITO INTEGRALS AND THEIR PROPERTIES
11 THE DIAGRAM FORMULA FOR PRODUCTS OF DEGENERATE U-STATISTICS
12 THE PROOF OF THE DIAGRAM FORMULA FOR U-STATISTICS
13 THE PROOF OF THEOREMS 8.3, 8.5 AND EXAMPLE 8.7
14 REDUCTION OF THE MAIN RESULT IN THIS WORK
15 THE STRATEGY OF THE PROOF FOR THE MAIN RESULT OF THIS WORK
16 A SYMMETRIZATION ARGUMENT
17 THE PROOF OF THE MAIN RESULT
18 AN OVERVIEW OF THE RESULTS AND A DISCUSSION OF THE LITERATURE
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
ON THE ESTIMATION OF MULTIPLE RANDOM INTEGRALS AND U-STATISTICS
/ MAJOR, PETER
: 2013
ABSTRACT / INHALTSTEXT
THIS WORK STARTS WITH THE STUDY OF THOSE LIMIT THEOREMS IN PROBABILITY
THEORY FOR WHICH CLASSICAL METHODS DO NOT WORK. IN MANY CASES SOME FORM
OF LINEARIZATION CAN HELP TO SOLVE THE PROBLEM, BECAUSE THE LINEARIZED
VERSION IS SIMPLER. BUT IN ORDER TO APPLY SUCH A METHOD WE HAVE TO SHOW
THAT THE LINEARIZATION CAUSES A NEGLIGIBLE ERROR. THE ESTIMATION OF THIS
ERROR LEADS TO SOME IMPORTANT LARGE DEVIATION TYPE PROBLEMS, AND THE
MAIN SUBJECT OF THIS WORK IS THEIR INVESTIGATION. WE PROVIDE SHARP
ESTIMATES OF THE TAIL DISTRIBUTION OF MULTIPLE INTEGRALS WITH RESPECT TO
A NORMALIZED EMPIRICAL MEASURE AND SO-CALLED DEGENERATE U-STATISTICS AND
ALSO OF THE SUPREMUM OF APPROPRIATE CLASSES OF SUCH QUANTITIES. THE
PROOFS APPLY A NUMBER OF USEFUL TECHNIQUES OF MODERN PROBABILITY THAT
ENABLE US TO INVESTIGATE THE NON-LINEAR FUNCTIONALS OF INDEPENDENT
RANDOM VARIABLES. THIS LECTURE NOTE YIELDS INSIGHTS INTO THESE METHODS,
AND MAY ALSO BE USEFUL FOR THOSE WHO ONLY WANT SOME NEW TOOLS TO HELP
THEM PROVE LIMIT THEOREMS WHEN STANDARD METHODS ARE NOT A VIABLE OPTION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Major, Péter |
| author_facet | Major, Péter |
| author_role | aut |
| author_sort | Major, Péter |
| author_variant | p m pm |
| building | Verbundindex |
| bvnumber | BV041194548 |
| classification_rvk | SI 850 SK 820 |
| classification_tum | MAT 604f MAT 606f MAT 000 |
| collection | ZDB-2-LNM ZDB-2-SMA |
| ctrlnum | (OCoLC)855563276 (DE-599)BVBBV041194548 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-37617-7 |
| format | Electronic eBook |
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| id | DE-604.BV041194548 |
| illustrated | Illustrated |
| indexdate | 2025-02-03T17:41:49Z |
| institution | BVB |
| isbn | 3642376169 9783642376177 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026169559 |
| oclc_num | 855563276 |
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| physical | 1 Online-Ressource (XIII, 288 S.) graph. Darst. |
| psigel | ZDB-2-LNM ZDB-2-SMA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spellingShingle | Major, Péter On the estimation of multiple random integrals and U-statistics Lecture notes in mathematics U-Statistik (DE-588)4754777-7 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| subject_GND | (DE-588)4754777-7 (DE-588)4126478-2 |
| title | On the estimation of multiple random integrals and U-statistics |
| title_auth | On the estimation of multiple random integrals and U-statistics |
| title_exact_search | On the estimation of multiple random integrals and U-statistics |
| title_full | On the estimation of multiple random integrals and U-statistics Péter Major |
| title_fullStr | On the estimation of multiple random integrals and U-statistics Péter Major |
| title_full_unstemmed | On the estimation of multiple random integrals and U-statistics Péter Major |
| title_short | On the estimation of multiple random integrals and U-statistics |
| title_sort | on the estimation of multiple random integrals and u statistics |
| topic | U-Statistik (DE-588)4754777-7 gnd Stochastisches Integral (DE-588)4126478-2 gnd |
| topic_facet | U-Statistik Stochastisches Integral |
| url | https://doi.org/10.1007/978-3-642-37617-7 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026169559&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026169559&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014303148 |
| work_keys_str_mv | AT majorpeter ontheestimationofmultiplerandomintegralsandustatistics |