Analysis of Stochastic Partial Differential Equations
Published by the AMS on behalf of CBMS Regional Conference Series in
Mathematics 119, Providence RI, 2014 (116 pp).
These are notes based on a 2013 NSF-CBMS course on stochastic partial differential equations.
The topics covered include a brief introduction to the stochastic heat equation, structure theory
for the linear stochastic heat equation, and an in-depth look at intermittency properties of the
solution to semilinear stochastic heat equations. Specific topics include stochastic integrals
a la Norbert Wiener, an infinite-dimensional Ito--type stochastic integral,
an example of a parabolic Anderson model, and intermittency fronts.
There are many possible approaches to stochastic PDEs. The selection of topics and techniques
presented here are informed by the guiding example of the stochastic heat equation.
A co-publication of the AMS and CBMS.
The list price is $29.60.
A Minicourse on Stochastic Partial Differential Equations
"Lecture Notes in Mathematics," Vol. 1962,
Springer, Berlin (paperback, 2008)
by Robert Dalang, Davar Khoshnevisan, David Nualart, Carl Mueller,
and Yimin Xiao, and edited by D. Khoshnevisan and Firas Rassoul-Agha.
Order form (29.95 €/44.95$)
Lectures based an NSF-funded minicourse on stochastic partial differential equations
at the University of Utah in 2006. Includes an introduction to SPDEs, analysis of hyperbolic
SPDEs, introduction to Malliavin calculus, duality and coupling, and fractal analysis.
Intended for graduate students and researchers.
List of errata (last update October 4, 2013) in
"Graduate Studies in Mathematics,"
American Mathematical Society, RI (hardback, 2007)
This is a graduate course in probability theory that is intended
primarily for a one-semester course, but can also be used for a
standard two-semester course.
The list price is $36 for AMS members, and $45 for
List of errata (last update Dec 16, 2013; more will be added soon) in
"Springer Monographs in Mathematics," Springer, NY (hardback , 2002;
This is a research-level book that lays the foundations of a theory of
multiparameter processes that has in mind applications to potential theory
for random fields and Hausdorff dimension computations.
List of errata (last update April 15, 2010) in