ENGLISH

Positive Harmonic Functions and Diffusion

By Ross G. Pinsky

Book information

Publisher
Cambridge University Press
Year
1995
ISBN
0521470145, 9780521470148
LCC
QA274.75 .P56 1995
Open Library ID
OL1087392M
Language
english
Format
DJVU
Filesize
3 MB (2740873 bytes)
Series
Cambridge Studies in Advanced Mathematics 45
Pages
490\490
Library
Kolxo3
DPI
300
Time added
2010-07-29 05:14:56

Description

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.

Similar books