A Course on Rough Paths: With an Introduction to Regularity Structures
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cham [u.a.]
Springer International Publishing
2014
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| Schriftenreihe: | Universitext
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| Schlagworte: | |
| Online-Zugang: | BTU01 FRO01 TUM01 UBA01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Beschreibung: | 1 Online-Ressource (XIV, 251 p. 2 illus) |
| ISBN: | 9783319083322 |
| DOI: | 10.1007/978-3-319-08332-2 |
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Datensatz im Suchindex
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| adam_text | A COURSE ON ROUGH PATHS
/ FRIZ, PETER K.
: 2014
TABLE OF CONTENTS / INHALTSVERZEICHNIS
INTRODUCTION
THE SPACE OF ROUGH PATHS
BROWNIAN MOTION AS A ROUGH PATH
INTEGRATION AGAINST ROUGH PATHS
STOCHASTIC INTEGRATION AND ITˆO’S FORMULA
DOOB–MEYER TYPE DECOMPOSITION FOR ROUGH PATHS
OPERATIONS ON CONTROLLED ROUGH PATHS
SOLUTIONS TO ROUGH DIFFERENTIAL EQUATIONS
STOCHASTIC DIFFERENTIAL EQUATIONS
GAUSSIAN ROUGH PATHS
CAMERON–MARTIN REGULARITY AND APPLICATIONS
STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS
INTRODUCTION TO REGULARITY STRUCTURES
OPERATIONS ON MODELLED DISTRIBUTIONS
APPLICATION TO THE KPZ EQUATION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
A COURSE ON ROUGH PATHS
/ FRIZ, PETER K.
: 2014
ABSTRACT / INHALTSTEXT
LYONS’ ROUGH PATH ANALYSIS HAS PROVIDED NEW INSIGHTS IN THE ANALYSIS
OF STOCHASTIC DIFFERENTIAL EQUATIONS AND STOCHASTIC PARTIAL DIFFERENTIAL
EQUATIONS, SUCH AS THE KPZ EQUATION. THIS TEXTBOOK PRESENTS THE FIRST
THOROUGH AND EASILY ACCESSIBLE INTRODUCTION TO ROUGH PATH ANALYSIS. WHEN
APPLIED TO STOCHASTIC SYSTEMS, ROUGH PATH ANALYSIS PROVIDES A MEANS TO
CONSTRUCT A PATHWISE SOLUTION THEORY WHICH, IN MANY RESPECTS, BEHAVES
MUCH LIKE THE THEORY OF DETERMINISTIC DIFFERENTIAL EQUATIONS AND
PROVIDES A CLEAN BREAK BETWEEN ANALYTICAL AND PROBABILISTIC ARGUMENTS.
IT PROVIDES A TOOLBOX ALLOWING TO RECOVER MANY CLASSICAL RESULTS WITHOUT
USING SPECIFIC PROBABILISTIC PROPERTIES SUCH AS PREDICTABILITY OR THE
MARTINGALE PROPERTY. THE STUDY OF STOCHASTIC PDES HAS RECENTLY LED TO A
SIGNIFICANT EXTENSION – THE THEORY OF REGULARITY STRUCTURES – AND
THE LAST PARTS OF THIS BOOK ARE DEVOTED TO A GENTLE INTRODUCTION. MOST
OF THIS COURSE IS WRITTEN AS AN ESSENTIALLY SELF-CONTAINED TEXTBOOK,
WITH AN EMPHASIS ON IDEAS AND SHORT ARGUMENTS, RATHER THAN PUSHING FOR
THE STRONGEST POSSIBLE STATEMENTS. A TYPICAL READER WILL HAVE BEEN
EXPOSED TO UPPER UNDERGRADUATE ANALYSIS COURSES AND HAS SOME INTEREST IN
STOCHASTIC ANALYSIS. FOR A LARGE PART OF THE TEXT, LITTLE MORE THAN ITO
INTEGRATION AGAINST BROWNIAN MOTION IS REQUIRED AS BACKGROUND
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Friz, Peter K. 1974- Hairer, Martin |
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| author_role | aut aut |
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| author_variant | p k f pk pkf m h mh |
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| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-08332-2 |
| format | Electronic eBook |
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| spelling | Friz, Peter K. 1974- Verfasser (DE-588)14055839X aut A Course on Rough Paths With an Introduction to Regularity Structures Peter K. Friz, Martin Hairer Cham [u.a.] Springer International Publishing 2014 1 Online-Ressource (XIV, 251 p. 2 illus) txt rdacontent c rdamedia cr rdacarrier Universitext Mathematik Mathematics Differential Equations Differential equations, partial Distribution (Probability theory) Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Lehrbuch (DE-588)4123623-3 gnd rswk-swf Stochastische Differenzengleichung (DE-588)4469723-5 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Lehrbuch (DE-588)4123623-3 s Stochastische Differenzengleichung (DE-588)4469723-5 s DE-604 Stochastische Differentialgleichung (DE-588)4057621-8 s 2\p DE-604 Hairer, Martin Verfasser aut Erscheint auch als Druckausgabe 978-3-319-08331-5 https://doi.org/10.1007/978-3-319-08332-2 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027514153&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027514153&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Friz, Peter K. 1974- Hairer, Martin A Course on Rough Paths With an Introduction to Regularity Structures Mathematik Mathematics Differential Equations Differential equations, partial Distribution (Probability theory) Stochastische Differentialgleichung (DE-588)4057621-8 gnd Lehrbuch (DE-588)4123623-3 gnd Stochastische Differenzengleichung (DE-588)4469723-5 gnd |
| subject_GND | (DE-588)4057621-8 (DE-588)4123623-3 (DE-588)4469723-5 |
| title | A Course on Rough Paths With an Introduction to Regularity Structures |
| title_auth | A Course on Rough Paths With an Introduction to Regularity Structures |
| title_exact_search | A Course on Rough Paths With an Introduction to Regularity Structures |
| title_full | A Course on Rough Paths With an Introduction to Regularity Structures Peter K. Friz, Martin Hairer |
| title_fullStr | A Course on Rough Paths With an Introduction to Regularity Structures Peter K. Friz, Martin Hairer |
| title_full_unstemmed | A Course on Rough Paths With an Introduction to Regularity Structures Peter K. Friz, Martin Hairer |
| title_short | A Course on Rough Paths |
| title_sort | a course on rough paths with an introduction to regularity structures |
| title_sub | With an Introduction to Regularity Structures |
| topic | Mathematik Mathematics Differential Equations Differential equations, partial Distribution (Probability theory) Stochastische Differentialgleichung (DE-588)4057621-8 gnd Lehrbuch (DE-588)4123623-3 gnd Stochastische Differenzengleichung (DE-588)4469723-5 gnd |
| topic_facet | Mathematik Mathematics Differential Equations Differential equations, partial Distribution (Probability theory) Stochastische Differentialgleichung Lehrbuch Stochastische Differenzengleichung |
| url | https://doi.org/10.1007/978-3-319-08332-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027514153&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=027514153&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT frizpeterk acourseonroughpathswithanintroductiontoregularitystructures AT hairermartin acourseonroughpathswithanintroductiontoregularitystructures |