Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs:
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| Main Author: | |
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2012
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121105-1108026-1-9 Inhaltsverzeichnis |
| Physical Description: | 123 S. graph. Darst. |
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| 100 | 1 | |a Pfaffel, Oliver |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs |c Oliver Pfaffel |
| 264 | 1 | |c 2012 | |
| 300 | |a 123 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 502 | |a München, Techn. Univ., Diss., 2012 | ||
| 650 | 0 | 7 | |a Eigenwert |0 (DE-588)4151200-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Matrix |0 (DE-588)4057624-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kovarianzmatrix |0 (DE-588)4165403-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
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| 689 | 0 | 1 | |a Kovarianzmatrix |0 (DE-588)4165403-1 |D s |
| 689 | 0 | 2 | |a Eigenwert |0 (DE-588)4151200-5 |D s |
| 689 | 0 | 3 | |a Stochastische Differentialgleichung |0 (DE-588)4057621-8 |D s |
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Record in the Search Index
| _version_ | 1804150177155514368 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1. INTRODUCTION 1
1.1. BACKGROUND AND MOTIVATION 1
1.2. OUTLINE O F THE THESIS 3
1 . EXTREME SINGULAR VALUES OF HEAVY-TAILED RANDOM MATRICES 7
2. LIMIT THEORY FOR THE LARGEST EIGENVALUES OF SAMPLE COVARIANCE
MATRICES 9 2.1. INTRODUCTION 9
2.2. MAIN RESULTS ON HEAVY-TAILED RANDOM MATRICES WITH DEPENDENT ENTRIES
12 2.2.1. A FIRST RESULT ON THE LARGEST EIGENVALUE 12
2.2.2. EXAMPLES AND DISCUSSION 15
2.2.3. EXTENSION TO RANDOM COEFFICIENT MODELS 16
2.3. PROOFS AND AUXILIARY RESULTS 17
2.3.1. A LARGE DEVIATION RESULT AND ITS CONSEQUENCES 17
2.3.2. CONVERGENCE IN OPERATOR NORM 21
2.3.3. EXTREMES OF DIAG(XX R ) 25
2.3.4. PROOF O F THEOREM 2.1 29
2.3.5. PROOF OF THEOREM 2.2 31
3. OBSERVATIONS WITH FINITE VARIANCE BUT INFINITE FOURTH MOMENT 35
3.1. INTRODUCTION AND MAIN RESULTS 35
3.2. PROOF 38
3.2.1. APPROXIMATION O F S BY ITS DIAGONAL 38
3.2.2. POINT PROCESS CONVERGENCE AND THE PROOF O F THEOREM 3.1 42
HTTP://D-NB.INFO/1034989383
IMAGE 2
3.2.3. PROOF O F THEOREM 3.2 47
4. RANDOM MATRICES WITH STRONGLY DEPENDENT ROWS AND COLUMNS 49
4.1. INTRODUCTION AND MAIN RESULTS 4 9
4.2. DEPENDENCE O F SUCCESSIVE ROWS 52
4.3. PROOF OF THE THEOREM 55
II. SPECTRAL DISTRIBUTION OF LIGHT-TAILED RANDOM MATRICES 61
5. SAMPLE COVARIANCE MATRICES OF LINEAR PROCESSES 63
5.1. INTRODUCTION AND MAIN RESULT 63
5.2. PROOFS 67
5.3. ILLUSTRATIVE EXAMPLES 75
5.3.1. AUTOREGRESSIVE MOVING AVERAGE PROCESSES 75
5.3.2. FRACTIONALLY INTEGRATED ARM A PROCESSES 78
6. A NEW RANDOM MATRIX MODEL WITH DEPENDENT ROWS AND COLUMNS 79
6.1. INTRODUCTION 79
6.2. A NEW RANDOM MATRIX MODEL 82
6.3. PROOF O F THEOREM 6.1 83
6.4. SKETCH OF AN ALTERNATIVE PROOF OF THEOREM 6.1 9 4
III. STRONG SOLUTIONS OF STOCHASTIC DIFFERENTIAL EQUATIONS 97
7. ON STRONG SOLUTIONS FOR POSITIVE DEFINITE JUMP DIFFUSIONS 99
7.1. INTRODUCTION 99
7.2. NOTATION AND GENERAL SET-UP 101
7.3. STATEMENT O F THE MAIN RESULTS 102
7.3.1. WISHART DIFFUSIONS WITH JUMPS 102
7.3.2. THE GENERAL SDE AND EXISTENCE RESULT 104
7.3.3. POSITIVE DEFINITE EXTENSIONS O F GENERALISED COX-INGERSOLL-ROSS
PRO
CESSES AND GARCH DIFFUSIONS 105
7.4. PROOFS 107
7.4.1. MCKEAN S ARGUMENT 108
7.4.2. PROOF OF THEOREM 7.1 109
7.5. CONCLUSION 113
BIBLIOGRAPHY 115
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| discipline | Mathematik |
| format | Thesis Book |
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| language | English |
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| spelling | Pfaffel, Oliver Verfasser aut Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs Oliver Pfaffel 2012 123 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2012 Eigenwert (DE-588)4151200-5 gnd rswk-swf Stochastische Matrix (DE-588)4057624-3 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Kovarianzmatrix (DE-588)4165403-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Stochastische Matrix (DE-588)4057624-3 s Kovarianzmatrix (DE-588)4165403-1 s Eigenwert (DE-588)4151200-5 s Stochastische Differentialgleichung (DE-588)4057621-8 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20121105-1108026-1-9 http://mediatum.ub.tum.de/node?id=1108026 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121105-1108026-1-9 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025873298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Pfaffel, Oliver Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs Eigenwert (DE-588)4151200-5 gnd Stochastische Matrix (DE-588)4057624-3 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Kovarianzmatrix (DE-588)4165403-1 gnd |
| subject_GND | (DE-588)4151200-5 (DE-588)4057624-3 (DE-588)4057621-8 (DE-588)4165403-1 (DE-588)4113937-9 |
| title | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs |
| title_auth | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs |
| title_exact_search | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs |
| title_full | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs Oliver Pfaffel |
| title_fullStr | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs Oliver Pfaffel |
| title_full_unstemmed | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs Oliver Pfaffel |
| title_short | Eigenvalues of large random matrices with dependent entries and strong solutions of SDEs |
| title_sort | eigenvalues of large random matrices with dependent entries and strong solutions of sdes |
| topic | Eigenwert (DE-588)4151200-5 gnd Stochastische Matrix (DE-588)4057624-3 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd Kovarianzmatrix (DE-588)4165403-1 gnd |
| topic_facet | Eigenwert Stochastische Matrix Stochastische Differentialgleichung Kovarianzmatrix Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1108026 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20121105-1108026-1-9 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025873298&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT pfaffeloliver eigenvaluesoflargerandommatriceswithdependententriesandstrongsolutionsofsdes |