Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth:
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| Format: | Thesis Book |
| Language: | English |
| Published: |
Passau
2020
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| Subjects: | |
| Online Access: | Volltext Volltext Inhaltsverzeichnis |
| Physical Description: | ii, 116 Seiten |
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| adam_text | 1 Contents 1 Introduction 1.1 Problem Description and Main Results........................................................ 1.2 Notations....................................................................................................... 1.3 Setting............................................................................................................. 1 1 4 6 2 Strong Approximations of Stochastic Differential Equations and Strong Asymptotic Optimality 9 2.1 Strong Approximations ............................................................................ 9 2.2 The Classes of Adaptive and of EquidistantApproximations...................... 12 2.3 Strong Asymptotic Optimality .................................................................... 13 3 Strongly Asymptotically Optimal Approximations with respect to the Supremum Error 17 3.1 Assumptions .................................................................................................. 18 3.2 Literature Review ............................................................................................ 20 3.3 The Equidistant and theAdaptive Tamed Euler Schemes .............................27 3.3.1 The Continuous-time Tamed Euler Schemes....................................... 28 3.3.2 The Equidistant Tamed Euler Schemes................................................28 3.3.3 The Adaptive Tamed Euler Schemes...................................................29 3.4 Main Results..................................................................................................... 30 3.5 Numerical
Experiment...................................................................................... 33 3.6 Proofs................................................................................................................. 36 3.6.1 Preliminaries......................................................................................... 36 3.6.2 Asymptotic Lower Bounds.....................................................................40 3.6.3 Asymptotic Upper Bounds .......................................................... 47 4 Strongly Asymptotically Optimal Approximations with respect to the Lp Error 53 4.1 Assumptions ................................................................................................. 54 4.2 Literature Review ......................................................................................... 56 4.3 The Equidistant and theAdaptive Tamed Milstein Schemes..........................66 4.3.1 The Continuous-time Tamed MilsteinSchemes.................................. 66 4.3.2 The Equidistant Tamed Milstein Schemes..........................................67
ii 4.4 4.5 4.6 4.7 4.3.3 The Adaptive Tamed Milstein Schemes ............................................ 68 Main Results................................................................................................. 69 Problems and Solution Approaches inthe Case p փ q.................................. 72 Numerical Experiment................................................................................... 74 Proofs.................................................................................................................77 4.7.1 Preliminaries...................................................................................... 78 4.7.2 Asymptotic Lower Bounds................................................................. 85 4.7.3 Asymptotic Upper Bounds ..................................................................90 5 Final Remarks and Outlook 95 A On some Properties ofSpecific Stochastic Processes 97 A.l Brownian Bridges.......................................................................................... 97 A.2 The Solution Process...................................................................................... 101 A.3 The Continuous-time Tamed Euler Schemes................................................ 103 A.4 The Continuous-time Tamed MilsteinSchemes............................................107 В Auxiliary Results 109 List of Figures 111 Bibliography 113
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| adam_txt |
1 Contents 1 Introduction 1.1 Problem Description and Main Results. 1.2 Notations. 1.3 Setting. 1 1 4 6 2 Strong Approximations of Stochastic Differential Equations and Strong Asymptotic Optimality 9 2.1 Strong Approximations . 9 2.2 The Classes of Adaptive and of EquidistantApproximations. 12 2.3 Strong Asymptotic Optimality . 13 3 Strongly Asymptotically Optimal Approximations with respect to the Supremum Error 17 3.1 Assumptions . 18 3.2 Literature Review . 20 3.3 The Equidistant and theAdaptive Tamed Euler Schemes .27 3.3.1 The Continuous-time Tamed Euler Schemes. 28 3.3.2 The Equidistant Tamed Euler Schemes.28 3.3.3 The Adaptive Tamed Euler Schemes.29 3.4 Main Results. 30 3.5 Numerical
Experiment. 33 3.6 Proofs. 36 3.6.1 Preliminaries. 36 3.6.2 Asymptotic Lower Bounds.40 3.6.3 Asymptotic Upper Bounds . 47 4 Strongly Asymptotically Optimal Approximations with respect to the Lp Error 53 4.1 Assumptions . 54 4.2 Literature Review . 56 4.3 The Equidistant and theAdaptive Tamed Milstein Schemes.66 4.3.1 The Continuous-time Tamed MilsteinSchemes. 66 4.3.2 The Equidistant Tamed Milstein Schemes.67
ii 4.4 4.5 4.6 4.7 4.3.3 The Adaptive Tamed Milstein Schemes . 68 Main Results. 69 Problems and Solution Approaches inthe Case p փ q. 72 Numerical Experiment. 74 Proofs.77 4.7.1 Preliminaries. 78 4.7.2 Asymptotic Lower Bounds. 85 4.7.3 Asymptotic Upper Bounds .90 5 Final Remarks and Outlook 95 A On some Properties ofSpecific Stochastic Processes 97 A.l Brownian Bridges. 97 A.2 The Solution Process. 101 A.3 The Continuous-time Tamed Euler Schemes. 103 A.4 The Continuous-time Tamed MilsteinSchemes.107 В Auxiliary Results 109 List of Figures 111 Bibliography 113 |
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| discipline_str_mv | Mathematik |
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| physical | ii, 116 Seiten |
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| spelling | Hatzesberger, Simon ca. 20./21. Jhd. Verfasser (DE-588)1217503269 aut Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth Simon Hatzesberger Passau 2020 ii, 116 Seiten txt rdacontent n rdamedia nc rdacarrier Dissertation Universität Passau 2020 Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Approximation (DE-588)4002498-2 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Stochastische Differentialgleichung (DE-588)4057621-8 s Approximation (DE-588)4002498-2 s DE-604 Erscheint auch als Online-Ausgabe URN: urn:nbn:de:bvb:739-opus4-8100 https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/810 kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-8100 Resolving-System kostenfrei Volltext Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032238456&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hatzesberger, Simon ca. 20./21. Jhd Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth Stochastische Differentialgleichung (DE-588)4057621-8 gnd Approximation (DE-588)4002498-2 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4002498-2 (DE-588)4113937-9 |
| title | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth |
| title_auth | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth |
| title_exact_search | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth |
| title_exact_search_txtP | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth |
| title_full | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth Simon Hatzesberger |
| title_fullStr | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth Simon Hatzesberger |
| title_full_unstemmed | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth Simon Hatzesberger |
| title_short | Strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super-linear growth |
| title_sort | strongly asymptotically optimal methods for the pathwise global approximation of the stochastic differential equations with coefficients of super linear growth |
| topic | Stochastische Differentialgleichung (DE-588)4057621-8 gnd Approximation (DE-588)4002498-2 gnd |
| topic_facet | Stochastische Differentialgleichung Approximation Hochschulschrift |
| url | https://opus4.kobv.de/opus4-uni-passau/frontdoor/index/index/docId/810 https://nbn-resolving.org/urn:nbn:de:bvb:739-opus4-8100 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=032238456&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hatzesbergersimon stronglyasymptoticallyoptimalmethodsforthepathwiseglobalapproximationofthestochasticdifferentialequationswithcoefficientsofsuperlineargrowth |