A minicourse on stochastic partial differential equations

Robert Dalang, Davar Khoshnevisan, Carl Mueller, David Nualart, Yimin Xiao (auth.), Davar Khoshnevisan, Firas Rassoul-Agha (eds.)3540859934, 9783540859932

In May 2006, The University of Utah hosted an NSF-funded minicourse on stochastic partial differential equations. The goal of this minicourse was to introduce graduate students and recent Ph.D.s to various modern topics in stochastic PDEs, and to bring together several experts whose research is centered on the interface between Gaussian analysis, stochastic analysis, and stochastic partial differential equations. This monograph contains an up-to-date compilation of many of those lectures. Particular emphasis is paid to showcasing central ideas and displaying some of the many deep connections between the mentioned disciplines, all the time keeping a realistic pace for the student of the subject.

Table of contents :
Front Matter….Pages I-XI
A Primer on Stochastic Partial Differential Equations….Pages 1-38
The Stochastic Wave Equation….Pages 39-71
Application of Malliavin Calculus to Stochastic Partial Differential Equations….Pages 73-109
Some Tools and Results for Parabolic Stochastic Partial Differential Equations….Pages 111-144
Sample Path Properties of Anisotropic Gaussian Random Fields….Pages 145-212
Back Matter….Pages 213-222