Coverart for item
The Resource Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear SPDEs II, by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic resource)

Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear SPDEs II, by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic resource)

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
by 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
http://library.link/vocab/creatorName
Chekroun, Mickaël D
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorName
  • Liu, Honghu.
  • Wang, Shouhong.
  • SpringerLink (Online service)
Series statement
SpringerBriefs in Mathematics,
http://library.link/vocab/subjectName
  • Mathematics
  • Dynamics
  • Ergodic theory
  • Differential equations
  • Partial differential equations
  • Probabilities
Label
Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear SPDEs II, by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-12520-6
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
978-3-319-12520-6
Dimensions
unknown
Extent
XVII, 129 p. 12 illus., 11 illus. in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319125206
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-12520-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086459292
Label
Stochastic Parameterizing Manifolds and Non-Markovian Reduced Equations : Stochastic Manifolds for Nonlinear SPDEs II, by Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic resource)
Link
http://ezproxy.eui.eu/login?url=http://dx.doi.org/10.1007/978-3-319-12520-6
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
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
978-3-319-12520-6
Dimensions
unknown
Extent
XVII, 129 p. 12 illus., 11 illus. in color.
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783319125206
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-319-12520-6
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1086459292

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