Borrow it
 African Studies Library
 Alumni Medical Library
 Astronomy Library
 Fineman and Pappas Law Libraries
 Frederick S. Pardee Management Library
 Howard Gotlieb Archival Research Center
 Mugar Memorial Library
 Music Library
 Pikering Educational Resources Library
 School of Theology Library
 Science & Engineering Library
 Stone Science Library
The Resource Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
Resource Information
The item Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 Summary
 This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or manmade complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee nonexplosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the ‘locally monotone case’ is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the wellknown case of globally monotone coefficients, substantially widens the applicability of the results. In addition, it leads to a unified approach and to simplified proofs in many classical examples. These include a large number of SPDEs not covered by the ‘globally monotone case’, such as, for exa mple, stochastic Burgers or stochastic 2D and 3D NavierStokes equations, stochastic CahnHilliard equations and stochastic surface growth models. To keep the book selfcontained and prerequisites low, necessary results about SDEs in finite dimensions are also included with complete proofs as well as a chapter on stochastic integration on Hilbert spaces. Further fundamentals (for example, a detailed account on the YamadaWatanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a oneyear graduate course
 Language
 eng
 Edition
 1st ed. 2015.
 Extent
 VI, 266 p.
 Contents

 Motivation, Aims and Examples
 Stochastic Integral in Hilbert Spaces
 SDEs in Finite Dimensions
 SDEs in Infinite Dimensions and Applications to SPDEs
 SPDEs with Locally Monotone Coefficients
 Mild Solutions
 Isbn
 9783319223544
 Label
 Stochastic Partial Differential Equations: An Introduction
 Title
 Stochastic Partial Differential Equations: An Introduction
 Statement of responsibility
 by Wei Liu, Michael Röckner
 Subject

 Differential equations
 Probability Theory and Stochastic Processes
 Differential equations
 Mathematical physics
 Probabilities
 Partial differential equations
 Ordinary Differential Equations
 Partial differential equations
 Game Theory, Economics, Social and Behav. Sciences
 Mathematical physics
 Game theory
 Probabilities
 Electronic resources
 Mathematics
 Game theory
 Mathematical Applications in the Physical Sciences
 Mathematics
 Game theory
 Partial Differential Equations
 Partial Differential Equations
 Language
 eng
 Summary
 This book provides an introduction to the theory of stochastic partial differential equations (SPDEs) of evolutionary type. SPDEs are one of the main research directions in probability theory with several wide ranging applications. Many types of dynamics with stochastic influence in nature or manmade complex systems can be modelled by such equations. The theory of SPDEs is based both on the theory of deterministic partial differential equations, as well as on modern stochastic analysis. Whilst this volume mainly follows the ‘variational approach’, it also contains a short account on the ‘semigroup (or mild solution) approach’. In particular, the volume contains a complete presentation of the main existence and uniqueness results in the case of locally monotone coefficients. Various types of generalized coercivity conditions are shown to guarantee nonexplosion, but also a systematic approach to treat SPDEs with explosion in finite time is developed. It is, so far, the only book where the latter and the ‘locally monotone case’ is presented in a detailed and complete way for SPDEs. The extension to this more general framework for SPDEs, for example, in comparison to the wellknown case of globally monotone coefficients, substantially widens the applicability of the results. In addition, it leads to a unified approach and to simplified proofs in many classical examples. These include a large number of SPDEs not covered by the ‘globally monotone case’, such as, for exa mple, stochastic Burgers or stochastic 2D and 3D NavierStokes equations, stochastic CahnHilliard equations and stochastic surface growth models. To keep the book selfcontained and prerequisites low, necessary results about SDEs in finite dimensions are also included with complete proofs as well as a chapter on stochastic integration on Hilbert spaces. Further fundamentals (for example, a detailed account on the YamadaWatanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a oneyear graduate course
 http://library.link/vocab/creatorName
 Liu, Wei
 Image bit depth
 0
 LC call number

 QA273.A1274.9
 QA274274.9
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName

 Röckner, Michael.
 SpringerLink
 Series statement
 Universitext,
 http://library.link/vocab/subjectName

 Mathematics
 Differential equations
 Partial differential equations
 Game theory
 Mathematical physics
 Probabilities
 Mathematics
 Probability Theory and Stochastic Processes
 Partial Differential Equations
 Ordinary Differential Equations
 Mathematical Applications in the Physical Sciences
 Game Theory, Economics, Social and Behav. Sciences
 Label
 Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
 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
 Motivation, Aims and Examples  Stochastic Integral in Hilbert Spaces  SDEs in Finite Dimensions  SDEs in Infinite Dimensions and Applications to SPDEs  SPDEs with Locally Monotone Coefficients  Mild Solutions
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 VI, 266 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319223544
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319223544
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319223544
 Label
 Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
 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
 Motivation, Aims and Examples  Stochastic Integral in Hilbert Spaces  SDEs in Finite Dimensions  SDEs in Infinite Dimensions and Applications to SPDEs  SPDEs with Locally Monotone Coefficients  Mild Solutions
 Dimensions
 unknown
 Edition
 1st ed. 2015.
 Extent
 VI, 266 p.
 File format
 multiple file formats
 Form of item
 electronic
 Isbn
 9783319223544
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code
 c
 Other control number
 10.1007/9783319223544
 Other physical details
 online resource.
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (DEHe213)9783319223544
Subject
 Differential equations
 Differential equations
 Electronic resources
 Game Theory, Economics, Social and Behav. Sciences
 Game theory
 Game theory
 Game theory
 Mathematical Applications in the Physical Sciences
 Mathematical physics
 Mathematical physics
 Mathematics
 Mathematics
 Ordinary Differential Equations
 Partial Differential Equations
 Partial Differential Equations
 Partial differential equations
 Partial differential equations
 Probabilities
 Probabilities
 Probability Theory and Stochastic Processes
Member of
Library Locations

African Studies LibraryBorrow it771 Commonwealth Avenue, 6th Floor, Boston, MA, 02215, US42.350723 71.108227


Astronomy LibraryBorrow it725 Commonwealth Avenue, 6th Floor, Boston, MA, 02445, US42.350259 71.105717

Fineman and Pappas Law LibrariesBorrow it765 Commonwealth Avenue, Boston, MA, 02215, US42.350979 71.107023

Frederick S. Pardee Management LibraryBorrow it595 Commonwealth Avenue, Boston, MA, 02215, US42.349626 71.099547

Howard Gotlieb Archival Research CenterBorrow it771 Commonwealth Avenue, 5th Floor, Boston, MA, 02215, US42.350723 71.108227


Music LibraryBorrow it771 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US42.350723 71.108227

Pikering Educational Resources LibraryBorrow it2 Silber Way, Boston, MA, 02215, US42.349804 71.101425

School of Theology LibraryBorrow it745 Commonwealth Avenue, 2nd Floor, Boston, MA, 02215, US42.350494 71.107235

Science & Engineering LibraryBorrow it38 Cummington Mall, Boston, MA, 02215, US42.348472 71.102257

Embed (Experimental)
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 faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/StochasticPartialDifferentialEquationsAn/4PkKFQVHQbo/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/StochasticPartialDifferentialEquationsAn/4PkKFQVHQbo/">Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</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 Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.bu.edu/portal/StochasticPartialDifferentialEquationsAn/4PkKFQVHQbo/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.bu.edu/portal/StochasticPartialDifferentialEquationsAn/4PkKFQVHQbo/">Stochastic Partial Differential Equations: An Introduction, by Wei Liu, Michael Röckner, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.bu.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.bu.edu/">Boston University Libraries</a></span></span></span></span></div>