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

• Autore: Prévôt Claudia
• Pubblicazione: Berlin, Germany ; ; New York, New York : , : Springer, , [2007]; ©2007
• Edizione: 1st ed. 2007.
• Descrizione fisica: 1 online resource (148 p.)
• Disciplina: 519.2
• Soggetto topico: Stochastic differential equations
• Persona (resp. second.): RöcknerMichael <1956->
• 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.
• Titolo autorizzato: A Concise Course on Stochastic Partial Differential Equations
• ISBN: 1-280-90216-7; 9786610902163; 3-540-70781-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910482992803321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1905