Positive Harmonic Functions and Diffusion (Cambridge Studies in Advanced Mathematics, Series Number 45) 1st Edition by Ross G. Pinsky (PDF)

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.

User’s Reviews

Editorial Reviews: Review Review of the hardback: ‘This book is reasonably self contained, accessible even to a graduate student but maintaining a high level of mathematical rigor.’ European Mathematical Society Newsletter Book Description A self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach.

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