UID:
almahu_9947363895302882
Umfang:
VI, 148 p.
,
online resource.
ISBN:
9783540707813
Serie:
Lecture Notes in Mathematics, 1905
Inhalt:
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.
Anmerkung:
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.
In:
Springer eBooks
Weitere Ausg.:
Printed edition: ISBN 9783540707806
Sprache:
Englisch
DOI:
10.1007/978-3-540-70781-3
URL:
http://dx.doi.org/10.1007/978-3-540-70781-3
