Positive Harmonic Functions and Diffusion
(Book #45 in the Cambridge Studies in Advanced Mathematics Series)
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Book Overview
In this book, Professor Pinsky gives a self-contained account of the construction and basic properties of diffusion processes, including both analytic and probabilistic techniques. He starts with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, and then develops the theory of the generalized principal eigenvalue and the related criticality theory for elliptic operators on arbitrary domains. He considers Martin boundary theory and calculates the Martin boundary for several classes of operators. The book provides an array of criteria for determining whether a diffusion process is transient or recurrent. Also introduced are the theory of bounded harmonic functions, and Brownian motion on a manifold. Many results that form the folklore of the subject are given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student.
Format:Hardcover
Language:English
ISBN:0521470145
ISBN13:9780521470148
Release Date:April 1995
Publisher:Cambridge University Press
Length:492 Pages
Weight:1.60 lbs.
Dimensions:1.2" x 6.2" x 9.3"
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