Positive Harmonic Functions and Diffusion (Paperback)

Ross G. Pinsky

ISBN 10: 0521059836 / ISBN 13: 9780521059831

Published by Cambridge University Press, Cambridge, 2008

About this Item

Paperback. In this book, Professor Pinsky gives a self-contained account of the theory of positive harmonic functions for second order elliptic operators, using an integrated probabilistic and analytic approach. The book begins with a treatment of the construction and basic properties of diffusion processes. This theory then serves as a vehicle for studying positive harmonic funtions. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author then develops the theory of the generalized principal eigenvalue, and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated 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 manifolds of negative curvature. Many results that form the folklore of the subject are here given a rigorous exposition, making this book a useful reference for the specialist, and an excellent guide for the graduate student. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Seller Inventory # 9780521059831

Bibliographic Details

• Title: Positive Harmonic Functions and Diffusion (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 2008
• Language: English
• ISBN 10: 0521059836
• ISBN 13: 9780521059831
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

Book Description

In this book Professor Pinsky gives a self contained account of the construction and basic properties of diffusion processes, and includes both analytic and probabilistic techniques. Starting with a rigorous treatment of the spectral theory of elliptic operators with nice coefficients on smooth, bounded domains, the author develops the theory of the generalised principal eigenvalue and the related criticality theory for elliptic operators on arbitrary domains. Martin boundary theory is considered, and the Martin boundary is explicitly calculated for several classes of operators. The book provides and 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 here given a rigorous exposition, making this book an useful reference for the specialist, and an excellent guide for the graduate student.