1.

Record Nr.

UNISA996466625903316

Autore

Prévôt Claudia

Titolo

A concise course on stochastic partial differential equations / / Claudia Prévôt, Michael Röckner

Pubbl/distr/stampa

Berlin, Germany ; ; New York, New York : , : Springer, , [2007]

©2007

ISBN

1-280-90216-7

9786610902163

3-540-70781-6

Edizione

[1st ed. 2007.]

Descrizione fisica

1 online resource (148 p.)

Collana

Lecture Notes in Mathematics, , 0075-8434 ; ; 1905

Disciplina

519.2

Soggetti

Stochastic differential equations

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references (p. 137-139) and index.

Nota di contenuto

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.

Sommario/riassunto

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.