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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Autor Corporativo: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2007.
|
| Edición: | 1st ed. 2007. |
| Colección: | Lecture Notes in Mathematics,
1905 |
| Temas: | |
| Acceso en línea: | Texto Completo |
MARC
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| 001 | 978-3-540-70781-3 | ||
| 003 | DE-He213 | ||
| 005 | 20220116021033.0 | ||
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| 020 | |a 9783540707813 |9 978-3-540-70781-3 | ||
| 024 | 7 | |a 10.1007/978-3-540-70781-3 |2 doi | |
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| 082 | 0 | 4 | |a 515 |2 23 |
| 100 | 1 | |a Prévôt, Claudia. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 245 | 1 | 2 | |a A Concise Course on Stochastic Partial Differential Equations |h [electronic resource] / |c by Claudia Prévôt, Michael Röckner. |
| 250 | |a 1st ed. 2007. | ||
| 264 | 1 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg : |b Imprint: Springer, |c 2007. | |
| 300 | |a VI, 148 p. |b online resource. | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a text file |b PDF |2 rda | ||
| 490 | 1 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 1905 | |
| 505 | 0 | |a Motivation, Aims and Examples -- Stochastic Integral in Hilbert spaces -- Stochastic Differential Equations in Finite Dimensions -- A Class of Stochastic Differential Equations in Banach Spaces -- Appendices: The Bochner Integral -- Nuclear and Hilbert-Schmidt Operators -- Pseudo Invers of Linear Operators -- Some Tools from Real Martingale Theory -- Weak and Strong Solutions: the Yamada-Watanabe Theorem -- Strong, Mild and Weak Solutions. | |
| 520 | |a 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. | ||
| 650 | 0 | |a Mathematical analysis. | |
| 650 | 0 | |a Differential equations. | |
| 650 | 0 | |a Probabilities. | |
| 650 | 1 | 4 | |a Analysis. |
| 650 | 2 | 4 | |a Differential Equations. |
| 650 | 2 | 4 | |a Probability Theory. |
| 700 | 1 | |a Röckner, Michael. |e author. |4 aut |4 http://id.loc.gov/vocabulary/relators/aut | |
| 710 | 2 | |a SpringerLink (Online service) | |
| 773 | 0 | |t Springer Nature eBook | |
| 776 | 0 | 8 | |i Printed edition: |z 9783540835288 |
| 776 | 0 | 8 | |i Printed edition: |z 9783540707806 |
| 830 | 0 | |a Lecture Notes in Mathematics, |x 1617-9692 ; |v 1905 | |
| 856 | 4 | 0 | |u https://doi.uam.elogim.com/10.1007/978-3-540-70781-3 |z Texto Completo |
| 912 | |a ZDB-2-SMA | ||
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| 950 | |a Mathematics and Statistics (SpringerNature-11649) | ||
| 950 | |a Mathematics and Statistics (R0) (SpringerNature-43713) | ||