On the estimation of jumps of continuous-time stochastic processes:
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| Format: | Thesis Book |
| Language: | English |
| Published: |
2013
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| Subjects: | |
| Online Access: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130318-1126101-0-5 Inhaltsverzeichnis |
| Physical Description: | XIV, 193 S. graph. Darst. |
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| 245 | 1 | 0 | |a On the estimation of jumps of continuous-time stochastic processes |c Florian Alexander Johann Ueltzhöfer |
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Record in the Search Index
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| adam_text | IMAGE 1
CONTENTS
1 INTRODUCTION L
2 SEMI-MARTINGALES, MARKOV PROCESSES, LIMIT THEOREMS G
2.1 RESUME OF THE GENERAL THEORY OF STOCHASTIC PROCESSES 9
2.1.1 RANDOM SETS; PROCESSES; OPTIONAL AND PREDICTABLE C-FIELD ... 9
2.1.2 STOPPING TIMES; PREDICTABLE TIMES; QUASI-LEFT CONTINUITY .... 11
2.1.3 MARTINGALES; INCREASING PROCESSES; DOOB-MEYER DECOMPOSITION 13
2.2 SEMI-MARTINGALES 14
2.2.1 SEMI-MARTINGALES; STOCHASTIC INTEGRALS; QUADRATIC VARIATION . . 14
2.2.2 RANDOM MEASURES; CHARACTERISTICS 16
2.2.3 ITO SEMI-MARTINGALES; ITO S FORMULA 17
2.3 TIGHTNESS; CONVERGENCE OF PROCESSES; LIMIT THEOREMS 20
2.3.1 TIGHTNESS 20
2.3.2 SKOROKHOD TOPOLOGY AND THE CONVERGENCE OF PROCESSES 21
2.3.3 MARTINGALE LIMIT THEOREMS 22
2.4 MARKOV CHAINS 23
2.4.1 IRREDUCIBILITY; SMALL SETS; PERIODICITY; FELLER CHAINS 24
2.4.2 RECURRENCE; INVARIANT MEASURE; ERGODICITY 27
2.5 MARKOV PROCESSES 29
2.5.1 R6SUM6 OF THE THEORY OF RAY PROCESSES; HUNT PROCESSES .... 29
2.5.2 RECURRENCE; ADDITIVE FUNCTIONALS; ERGODIC THEOREMS 33
2.5.3 DETERMINISTIC EQUIVALENTS; DARLING-KAC S CONDITION; MITTAGLEFFLER
PROCESS 35
2.5.4 JUMPS OF MARKOV PROCESSES; LEVY SYSTEM; LEVY KERNEL 36
XI
HTTP://D-NB.INFO/1038239001
IMAGE 2
CONTENTS
ESTIMATION OF JUMPS BEYOND THE LEVY CASE 3G
3 ON NON-PARAMETRIC ESTIMATION OF THE LEVY KERNEL OF MARKOV PROCESSES 41
3.1 INTRODUCTION 41
3.2 ESTIMATION FROM HIGH-FREQUENCY OBSERVATIONS 44
3.2.1 PRELIMINARIES AND ASSUMPTIONS . 44
3.2.2 KERNEL DENSITY ESTIMATOR 46
3.2.3 CONSISTENCY AND CENTRAL LIMIT THEOREM 47
3.3 ESTIMATION FROM CONTINUOUS-TIME OBSERVATIONS 52
3.3.1 PRELIMINARIES AND ASSUMPTIONS 52
3.3.2 KERNEL DENSITY ESTIMATOR 53
3.3.3 CONSISTENCY AND CENTRAL LIMIT THEOREM 54
3.4 PROOFS FOR RESULTS OF SECTION 3.3 56
3.4.1 AN EXTENSION OF BIRKHOFF S THEOREM 57
3.4.2 THE AUXILIARY MARKOV CHAINS 60
3.4.3 PROOF OF THEOREM 3.3.6 63
3.4.4 PROOFS OF THEOREM 3.3.7 AND COROLLARY 3.3.8 67
3.5 PROOFS FOR RESULTS OF SECTION 3.2 78
3.5.1 SMALL-TIME ASYMPTOTIC AND SOJOURN TIME DISCRETISATION ERROR . . 79
3.5.2 AUXILIARY MARTINGALE LIMIT THEOREM 92
3.5.3 PROOF OF THEOREM 3.2.9 93
3.5.4 PROOFS OF THEOREM 3.2.10 AND COROLLARY 3.2.11 97
3.6 ON THE AUXILIARY MARKOV CHAINS Z AND Z 101
4 ON THE ESTIMATION OF THE LEVY MEASURE OF TIME-CHANGED LEVY PROCESSES
105
4.1 INTRODUCTION 105
4.2 ESTIMATION FROM HIGH-FREQUENCY OBSERVATIONS 106
4.2.1 PRELIMINARIES AND ASSUMPTIONS 106
4.2.2 KERNEL DENSITY ESTIMATOR 107
4.2.3 CONSISTENCY AND CENTRAL LIMIT THEOREM 108
4.3 PROOFS 110
XII
IMAGE 3
CONTENTS
ESTIMATION OF JUMPS IN PRACTICE 117
5 SIMULATION STUDIES 119
5.1 MARKOVIAN ITO SEMI-MARTINGALES 119
5.1.1 THE FINITE ACTIVITY CASE 121
5.1.2 THE INFINITE ACTIVITY CASE 154
5.2 PENALISED PROJECTION ESTIMATION OF THE LEVY DENSITY OF LEVY
PROCESSES 161
6 EMPIRICAL MODELLING OF THE INTERMITTENCY IN ATMOSPHERIC TURBULENCE 169
6.1 INTRODUCTION 169
6.2 THE INTERMITTENCY MODEL AND ITS ESTIMATION 173
6.2.1 MODELLING FRAMEWORK 173
6.2.2 ESTIMATION FROM DISCRETE OBSERVATIONS 175
6.3 AN EMPIRICAL STUDY OF THE BROOKHAVEN WIND SPEED DATA SET 179
6.4 SIMULATION STUDY 182
BIBLIOGRAPHY 187
XIII
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| any_adam_object | 1 |
| author | Ueltzhöfer, Florian Alexander Johann |
| author_facet | Ueltzhöfer, Florian Alexander Johann |
| author_role | aut |
| author_sort | Ueltzhöfer, Florian Alexander Johann |
| author_variant | f a j u faj faju |
| building | Verbundindex |
| bvnumber | BV040953984 |
| classification_tum | MAT 607d MAT 634d |
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| ctrlnum | (OCoLC)844069401 (DE-599)BVBBV040953984 |
| 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 |
| format | Thesis Book |
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| spelling | Ueltzhöfer, Florian Alexander Johann Verfasser aut On the estimation of jumps of continuous-time stochastic processes Florian Alexander Johann Ueltzhöfer 2013 XIV, 193 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 Sprungprozess (DE-588)4427906-1 gnd rswk-swf Kernschätzung (DE-588)4353527-6 gnd rswk-swf Zentraler Grenzwertsatz (DE-588)4067618-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Sprungprozess (DE-588)4427906-1 s Kernschätzung (DE-588)4353527-6 s Zentraler Grenzwertsatz (DE-588)4067618-3 s DE-604 Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130318-1126101-0-5 http://mediatum.ub.tum.de/node?id=1126101 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130318-1126101-0-5 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025932468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ueltzhöfer, Florian Alexander Johann On the estimation of jumps of continuous-time stochastic processes Sprungprozess (DE-588)4427906-1 gnd Kernschätzung (DE-588)4353527-6 gnd Zentraler Grenzwertsatz (DE-588)4067618-3 gnd |
| subject_GND | (DE-588)4427906-1 (DE-588)4353527-6 (DE-588)4067618-3 (DE-588)4113937-9 |
| title | On the estimation of jumps of continuous-time stochastic processes |
| title_auth | On the estimation of jumps of continuous-time stochastic processes |
| title_exact_search | On the estimation of jumps of continuous-time stochastic processes |
| title_full | On the estimation of jumps of continuous-time stochastic processes Florian Alexander Johann Ueltzhöfer |
| title_fullStr | On the estimation of jumps of continuous-time stochastic processes Florian Alexander Johann Ueltzhöfer |
| title_full_unstemmed | On the estimation of jumps of continuous-time stochastic processes Florian Alexander Johann Ueltzhöfer |
| title_short | On the estimation of jumps of continuous-time stochastic processes |
| title_sort | on the estimation of jumps of continuous time stochastic processes |
| topic | Sprungprozess (DE-588)4427906-1 gnd Kernschätzung (DE-588)4353527-6 gnd Zentraler Grenzwertsatz (DE-588)4067618-3 gnd |
| topic_facet | Sprungprozess Kernschätzung Zentraler Grenzwertsatz Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1126101 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130318-1126101-0-5 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025932468&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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