Partial Differential Equations for Probabilists

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Daniel W. StroockCambridge University Press, 5/29/2008EAN 9780521886512, ISBN10: 0521886511Hardcover, 232 pages, 22.9 x 15.2 x 1.8 cmLanguage: EnglishThis 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 readily accessible to 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 types. 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 De Giorgi–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.1. Kolmogorov's forward, basic results2. Non-elliptic regularity results3. Preliminary elliptic regularity results4. Nash theory5. Localization6. On a manifold7. Subelliptic estimates and Hörmander's theorem. Show more