Stochastic partial differential equations : an introduction
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The work Stochastic partial differential equations : an introduction represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
The Resource
Stochastic partial differential equations : an introduction
Resource Information
The work Stochastic partial differential equations : an introduction represents a distinct intellectual or artistic creation found in University of Oklahoma Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Stochastic partial differential equations : an introduction
 Title remainder
 an introduction
 Statement of responsibility
 Wei Liu, Michael Röckner
 Subject

 Stochastic partial differential equations
 Electronic books
 Mathematical Statistics
 Mathematical modelling
 Differential calculus & equations
 Physical Sciences & Mathematics
 Game theory
 Probability & statistics
 Mathematics  Probability & Statistics  General
 Mathematics  Applied
 Mathematics  Differential Equations
 Stochastic partial differential equations
 Mathematics
 Mathematics  Game 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
 Cataloging source
 YDXCP
 Dewey number
 515/.353
 Index
 index present
 LC call number

 QA274.25
 QA273.A1274.9
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Universitext,
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