TY  - BOOK
AU  - 
AU  - 
ED  - SpringerLink (Online service)
TI  - A Concise Course on Stochastic Partial Differential Equations
T2  - Lecture Notes in Mathematics,
SN  - 9783540707813
AV  - QA370-380 
U1  - 515.353 23
PY  - 2007///
CY  - Berlin, Heidelberg
PB  - Springer Berlin Heidelberg
KW  - Mathematics
KW  - Differential equations, partial
KW  - Distribution (Probability theory)
KW  - Partial Differential Equations
KW  - Probability Theory and Stochastic Processes
N1  - 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; ZDB-2-SMA; ZDB-2-LNM
N2  - 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
UR  - http://dx.doi.org/10.1007/978-3-540-70781-3
ER  -