About this book
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.
- DOI https://doi.org/10.1007/978-3-540-70781-3
- Copyright Information Springer-Verlag Berlin Heidelberg 2007
- Publisher Name Springer, Berlin, Heidelberg
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-540-70780-6
- Online ISBN 978-3-540-70781-3
- Series Print ISSN 0075-8434
- Series Online ISSN 1617-9692
- About this book