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A concise course on stochastic partial differential equations

These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the cas...

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Detalles Bibliográficos
Autores principales: Prévôt, Claudia, Röckner, Michael
Lenguaje:eng
Publicado: Springer 2007
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-3-540-70781-3
http://cds.cern.ch/record/1691699
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author Prévôt, Claudia
Röckner, Michael
author_facet Prévôt, Claudia
Röckner, Michael
author_sort Prévôt, Claudia
collection CERN
description These lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.
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spelling cern-16916992021-04-21T21:07:48Zdoi:10.1007/978-3-540-70781-3http://cds.cern.ch/record/1691699engPrévôt, ClaudiaRöckner, MichaelA concise course on stochastic partial differential equationsMathematical Physics and MathematicsThese lectures concentrate on (nonlinear) stochastic partial differential equations (SPDE) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modelled by such equations. To keep the technicalities minimal we confine ourselves to the case where the noise term is given by a stochastic integral w.r.t. a cylindrical Wiener process.But all results can be easily generalized to SPDE with more general noises such as, for instance, stochastic integral w.r.t. a continuous local martingale. There are basically three approaches to analyze SPDE: the "martingale measure approach", the "mild solution approach" and the "variational approach". The purpose of these notes is to give a concise and as self-contained as possible an introduction to the "variational approach". A large part of necessary background material, such as definitions and results from the theory of Hilbert spaces, are included in appendices.Springeroai:cds.cern.ch:16916992007
spellingShingle Mathematical Physics and Mathematics
Prévôt, Claudia
Röckner, Michael
A concise course on stochastic partial differential equations
title A concise course on stochastic partial differential equations
title_full A concise course on stochastic partial differential equations
title_fullStr A concise course on stochastic partial differential equations
title_full_unstemmed A concise course on stochastic partial differential equations
title_short A concise course on stochastic partial differential equations
title_sort concise course on stochastic partial differential equations
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/978-3-540-70781-3
http://cds.cern.ch/record/1691699
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