This book deals with equations that have played a central role in the interplay between partial differential equations and probability theory. Most of thismaterial 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 partialdifferential equations of parabolic and elliptic type. Many of the techniqueshave 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 Hormander. INDICE: 1. Kolmogorov's forward, basic results; 2. Non-elliptic regularityresults; 3. Preliminary elliptic regularity results; 4. Nash theory; 5. Localization; 6. On a manifold; 7. Subelliptic estimates and Hormander's theorem.
- ISBN: 978-1-10-740052-8
- Editorial: Cambridge University
- Encuadernacion: Cartoné
- Páginas: 224
- Fecha Publicación: 28/04/2008
- Nº Volúmenes: 1
- Idioma: Inglés