Stochastic manifolds for nonlinear SPDEs: 2 Stochastic parameterizing manifolds and non-markovian reduced equations
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| Main Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham [u.a.]
Springer
2015
|
| Series: | SpringerBriefs in mathematics
SpringerBriefs in mathematics |
| Online Access: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Inhaltsverzeichnis Abstract |
| Physical Description: | 1 Online-Ressource |
| ISBN: | 9783319125190 9783319125206 |
| DOI: | 10.1007/978-3-319-12520-6 |
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Record in the Search Index
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|---|---|
| adam_text | STOCHASTIC PARAMETERIZING MANIFOLDS AND NON-MARKOVIAN REDUCED EQUATIONS
/ CHEKROUN, MICKAEL D.
: 2015
TABLE OF CONTENTS / INHALTSVERZEICHNIS
GENERAL INTRODUCTION
PRELIMINARIES
INVARIANT MANIFOLDS
PULLBACK CHARACTERIZATION OF APPROXIMATING, AND PARAMETERIZING MANIFOLDS
NON-MARKOVIAN STOCHASTIC REDUCED EQUATIONS
ON-MARKOVIAN STOCHASTIC REDUCED EQUATIONS ON THE FLY
PROOF OF LEMMA 5.1.-REFERENCES
INDEX.
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
STOCHASTIC PARAMETERIZING MANIFOLDS AND NON-MARKOVIAN REDUCED EQUATIONS
/ CHEKROUN, MICKAEL D.
: 2015
ABSTRACT / INHALTSTEXT
IN THIS SECOND VOLUME, A GENERAL APPROACH IS DEVELOPED TO PROVIDE
APPROXIMATE PARAMETERIZATIONS OF THE SMALL SCALES BY THE LARGE ONES
FOR A BROAD CLASS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS (SPDES).
THIS IS ACCOMPLISHED VIA THE CONCEPT OF PARAMETERIZING MANIFOLDS (PMS),
WHICH ARE STOCHASTIC MANIFOLDS THAT IMPROVE, FOR A GIVEN REALIZATION OF
THE NOISE, IN MEAN SQUARE ERROR THE PARTIAL KNOWLEDGE OF THE FULL SPDE
SOLUTIONWHEN COMPARED TO ITS PROJECTION ONTO SOME RESOLVED
MODES.BACKWARD-FORWARD SYSTEMS ARE DESIGNED TO GIVE ACCESS TO SUCH PMS
IN PRACTICE. THE KEY IDEA CONSISTS OF REPRESENTING THE MODES WITH HIGH
WAVE NUMBERS AS A PULLBACK LIMIT DEPENDING ON THE TIME-HISTORY OF THE
MODES WITH LOW WAVE NUMBERS.NON-MARKOVIAN STOCHASTIC REDUCED SYSTEMS
ARE THEN DERIVED BASED ON SUCH A PM APPROACH. THE REDUCED SYSTEMS TAKE
THE FORM OF STOCHASTIC DIFFERENTIAL EQUATIONS INVOLVING RANDOM
COEFFICIENTS THAT CONVEY MEMORY EFFECTS. THE THEORY IS ILLUSTRATED ON A
STOCHASTIC BURGERS-TYPE EQUATION
DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
|
| any_adam_object | 1 |
| author | Chekroun, Mickaël D. 1975- Liu, Honghu Wang, Shouhong 1962- |
| author_GND | (DE-588)1065186134 (DE-588)1065186770 (DE-588)1065187831 |
| author_facet | Chekroun, Mickaël D. 1975- Liu, Honghu Wang, Shouhong 1962- |
| author_role | aut aut aut |
| author_sort | Chekroun, Mickaël D. 1975- |
| author_variant | m d c md mdc h l hl s w sw |
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| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-319-12520-6 |
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| spelling | Chekroun, Mickaël D. 1975- Verfasser (DE-588)1065186134 aut Stochastic manifolds for nonlinear SPDEs 2 Stochastic parameterizing manifolds and non-markovian reduced equations Mickaël D. Chekroun ; Honghu Liu ; Shouhong Wang Cham [u.a.] Springer 2015 1 Online-Ressource txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in mathematics Liu, Honghu Verfasser (DE-588)1065186770 aut Wang, Shouhong 1962- Verfasser (DE-588)1065187831 aut (DE-604)BV042276788 2 https://doi.org/10.1007/978-3-319-12520-6 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027714260&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=027714260&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Abstract |
| spellingShingle | Chekroun, Mickaël D. 1975- Liu, Honghu Wang, Shouhong 1962- Stochastic manifolds for nonlinear SPDEs |
| title | Stochastic manifolds for nonlinear SPDEs |
| title_auth | Stochastic manifolds for nonlinear SPDEs |
| title_exact_search | Stochastic manifolds for nonlinear SPDEs |
| title_full | Stochastic manifolds for nonlinear SPDEs 2 Stochastic parameterizing manifolds and non-markovian reduced equations Mickaël D. Chekroun ; Honghu Liu ; Shouhong Wang |
| title_fullStr | Stochastic manifolds for nonlinear SPDEs 2 Stochastic parameterizing manifolds and non-markovian reduced equations Mickaël D. Chekroun ; Honghu Liu ; Shouhong Wang |
| title_full_unstemmed | Stochastic manifolds for nonlinear SPDEs 2 Stochastic parameterizing manifolds and non-markovian reduced equations Mickaël D. Chekroun ; Honghu Liu ; Shouhong Wang |
| title_short | Stochastic manifolds for nonlinear SPDEs |
| title_sort | stochastic manifolds for nonlinear spdes stochastic parameterizing manifolds and non markovian reduced equations |
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