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Stochastic partial differential equa...

Liu, Wei.

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Stochastic partial differential equations = an introduction /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Stochastic partial differential equations/ by Wei Liu, Michael Rockner.
Reminder of title:	an introduction /
Author:	Liu, Wei.
other author:	Rockner, Michael.
Published:	Cham :Springer International Publishing : : 2015.,
Description:	vi, 266 p. :ill., digital ;24 cm.
[NT 15003449]:	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.
Contained By:	Springer eBooks
Subject:	Stochastic partial differential equations. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-22354-4
ISBN:	9783319223544

Stochastic partial differential equations = an introduction /
Liu, Wei.

Stochastic partial differential equationsan introduction /[electronic resource] :by Wei Liu, Michael Rockner. - Cham :Springer International Publishing :2015. - vi, 266 p. :ill., digital ;24 cm. - Universitext,0172-5939. - Universitext..

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.

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 man-made 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 non-explosion, 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 well-known 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 Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic surface growth models. To keep the book self-contained 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 Yamada-Watanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a one-year graduate course.

ISBN: 9783319223544

Standard No.: 10.1007/978-3-319-22354-4doiSubjects--Topical Terms:

625093
Stochastic partial differential equations.

LC Class. No.: QA274.25

Dewey Class. No.: 515.353

Stochastic partial differential equations = an introduction /
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245 1 0 $a Stochastic partial differential equations $h [electronic resource] : $b an introduction / $c by Wei Liu, Michael Rockner.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2015.
300 $a vi, 266 p. : $b ill., digital ; $c 24 cm.
490 1 $a Universitext, $x 0172-5939
505 0 $a 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.
520 $a 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 man-made 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 non-explosion, 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 well-known 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 Navier-Stokes equations, stochastic Cahn-Hilliard equations and stochastic surface growth models. To keep the book self-contained 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 Yamada-Watanabe theorem in infinite dimensions) used in the book have added proofs in the appendix. The book can be used as a textbook for a one-year graduate course.
650 0 $a Stochastic partial differential equations. $3 625093
650 1 4 $a Mathematics. $3 515831
650 2 4 $a Probability Theory and Stochastic Processes. $3 891080
650 2 4 $a Partial Differential Equations. $3 890899
650 2 4 $a Ordinary Differential Equations. $3 891264
650 2 4 $a Mathematical Applications in the Physical Sciences. $3 1566152
650 2 4 $a Game Theory, Economics, Social and Behav. Sciences. $3 891103
700 1 $a Rockner, Michael. $3 905859
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856 4 0 $u http://dx.doi.org/10.1007/978-3-319-22354-4
950 $a Mathematics and Statistics (Springer-11649)