A Concise Course on Stochastic Partial Differential Equations

• Main Authors: Prévôt, Claudia (Author), Röckner, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Lecture Notes in Mathematics, 1905
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Probabilities.; Analysis.; Partial Differential Equations.; Probability Theory and Stochastic Processes.

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 cas...

Table of 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.