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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 University of Oklahoma 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 University of Oklahoma 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
 1 online resource (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
 9783319223537
 Label
 Stochastic Partial Differential Equations: An Introduction
 Title
 Stochastic Partial Differential Equations: An Introduction
 Statement of responsibility
 by Wei Liu, Michael Röckner
 Subject

 Game Theory, Economics, Social and Behav. Sciences
 Mathematical Applications in the Physical Sciences
 Mathematics
 Ordinary Differential Equations
 Partial Differential Equations
 Probability Theory and Stochastic Processes
 Differential Equations
 Differential equations, partial
 Distribution (Probability theory
 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
 Dewey number
 519.2
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut

 x9_IApqmRU
 EZfdzvN0Ri8
 Image bit depth
 0
 LC call number

 QA273.A1274.9
 QA274274.9
 Literary form
 non fiction
 http://library.link/vocab/relatedWorkOrContributorName
 Röckner, Michael.
 Series statement
 Universitext,
 http://library.link/vocab/subjectName

 Distribution (Probability theory
 Differential equations, partial
 Differential Equations
 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
 1 online resource (VI, 266 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9783319223537
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319223544
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (DEHe213)9783319223544
 (EXLCZ)993710000000521694
 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
 1 online resource (VI, 266 p.)
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9783319223537
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783319223544
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number

 (DEHe213)9783319223544
 (EXLCZ)993710000000521694
Subject
 Game Theory, Economics, Social and Behav. Sciences
 Mathematical Applications in the Physical Sciences
 Mathematics
 Ordinary Differential Equations
 Partial Differential Equations
 Probability Theory and Stochastic Processes
 Differential Equations
 Differential equations, partial
 Distribution (Probability theory
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