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On the estimation of jumps of continuous-time stochastic processes:

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Bibliographic Details
Main Author:	Ueltzhöfer, Florian Alexander Johann (Author)
Format:	Thesis/Dissertation Book
Language:	English
Published:	2013
Subjects:	Sprungprozess Kernschätzung Zentraler Grenzwertsatz Hochschulschrift
Links:	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
Physical Description:	XIV, 193 S. graph. Darst.

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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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author	Ueltzhöfer, Florian Alexander Johann
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dewey-tens	510 - Mathematics
discipline	Mathematik
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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
work_keys_str_mv	AT ueltzhoferflorianalexanderjohann ontheestimationofjumpsofcontinuoustimestochasticprocesses

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