Partial Differential Equations for Probabilists

Erscheinungsjahr 2010
ISBN: 978-0-521-88651-2
Verlag: Cambridge University Press

Buch, Englisch, Band 112, 224 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 533 g

Reihe: Cambridge Studies in Advanced Mathematics

This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of this material has been treated elsewhere, but it is rarely presented in a manner that makes it easy to understand for people whose background is probability theory. Many results are given new proofs designed for readers with limited expertise in analysis. The author covers the theory of linear, second order partial differential equations of parabolic and elliptic type. Many of the techniques have antecedents in probability theory, although the book also covers a few purely analytic techniques. In particular, a chapter is devoted to the DeGiorgi-Moser-Nash estimates and the concluding chapter gives an introduction to the theory of pseudodifferential operators and their application to hypoellipticity, including the famous theorem of Lars Hörmander.

Autoren/Hrsg.

Stroock, Daniel W.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

1. Kolmogorov's forward, basic results
2. Non-elliptic regularity results
3. Preliminary elliptic regularity results
4. Nash theory
5. Localization
6. On a manifold
7. Subelliptic estimates and Hörmander's theorem.

Über Autor(innen)

Stroock, Daniel W.
Daniel W. Stroock is the Simons Professor of Mathematics at the Massachusetts Institute of Technology. His introduction to the study of partial differential equations was at the Courant Institute of Mathematical Sciences in courses by L. Nirenberg, P. Lax, and F. John. He is a member of the National Academy of Sciences and was the recipient of the 1996 AMS Steele Prize for seminal research together with S. R. S. Varadhan. This is Professor Stroock's seventh book.