A Concise Course on Stochastic Partial Differential Equations / by Claudia Prévôt, Michael Röckner.

Format:

Book

Author/Creator:

Prévôt, Claudia, author.

Röckner, Michael, 1956- author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1905.

Lecture Notes in Mathematics, 0075-8434 ; 1905

Language:

English

Subjects (All):

Global analysis (Mathematics).

Differential equations, Partial.

Distribution (Probability theory).

Analysis.

Partial Differential Equations.

Probability Theory and Stochastic Processes.

Local Subjects:

Analysis.

Partial Differential Equations.

Probability Theory and Stochastic Processes.

Physical Description:

1 online resource (VI, 148 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9783540707813

Access Restriction:

Restricted for use by site license.