From Lévy-Type Processes to Parabolic SPDEs

Advanced Courses in CRM-Barcelona, CRM-Birkhäuser, Basel, 2017; (with René Schilling; Frederic Utzet and Lluis Quer-Sardanyons, ed.s).
Cover photo These are notes based on a CRM course that René Schilling and I gave in 2014, and are written in collaboration with René Schilling.
The list price is $39.99 at the Springer bookstore.

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).
Cover photo 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.
  • AMS bookstore book link

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$)
Cover photo 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 PDF.
  • Table of contents in PDF.


"Graduate Studies in Mathematics," American Mathematical Society, RI (hardback, 2007)
Cover photo 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 nonmembers.
  • List of errata (last update Dec 16, 2013; more will be added soon) in PDF
  • Table of contents in PDF
  • AMS bookstore book link
  • Reviews: Z-Math

Multiparameter Processes

"Springer Monographs in Mathematics," Springer, NY (hardback , 2002; paperback, 2010)
Cover photo 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.

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