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)
Resource Information
The item Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- 1 online resource (xvii, 129 pages)
- 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
- Isbn
- 9783319125190
- 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
- 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
- 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)
- 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)
- 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
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Stochastic-parameterizing-manifolds-and/BQjxbYedTG4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Stochastic-parameterizing-manifolds-and/BQjxbYedTG4/">Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data - Experimental
Data Citation of the Item Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Stochastic-parameterizing-manifolds-and/BQjxbYedTG4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Stochastic-parameterizing-manifolds-and/BQjxbYedTG4/">Stochastic parameterizing manifolds and non-markovian reduced equations : stochastic manifolds for nonlinear SPDEs II, Mickaël D. Chekroun, Honghu Liu, Shouhong Wang, (electronic book)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
