Coverart for item
The Resource Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)

Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)

Label
Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II
Title
Stochastic parameterizing manifolds and non-markovian reduced equations
Title remainder
stochastic manifolds for nonlinear SPDEs II
Statement of responsibility
Mickaël D. Chekroun, Honghu Liu, Shouhong Wang
Creator
Contributor
Author
Subject
Language
eng
Summary
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 solution when 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
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Chekroun, Mickaël D
Dewey number
515/.353
Illustrations
illustrations
Index
index present
LC call number
QA274.25
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Liu, Honghu
  • Wang, Shouhong
Series statement
SpringerBriefs in Mathematics,
http://library.link/vocab/subjectName
Stochastic partial differential equations
Label
Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
SPR898892936
Dimensions
unknown
Extent
1 online resource (xvii, 129 pages)
File format
unknown
Form of item
online
Isbn
9783319125190
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-12520-6
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote
Label
Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
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
Control code
SPR898892936
Dimensions
unknown
Extent
1 online resource (xvii, 129 pages)
File format
unknown
Form of item
online
Isbn
9783319125190
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-3-319-12520-6
Other physical details
illustrations (some color).
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote

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