Positive Harmonic Functions and Diffusion

By: Ross G. Pinsky

Write A Review

Paperback | 24 April 2008

At a Glance

Paperback
492 Pages

Dimensions(cm)
15.2 x 23.0 x 3.1

Paperback

RRP $159.95

$142.99

11%OFF

or 4 interest-free payments of $35.75 with

Ships in 5 to 7 business days

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.

Industry Reviews

From the hardback review: 'This book is reasonably self contained, accessible even to a graduate student but maintaining a high level of mathematical rigor.' European Mathematical Society Newsletter

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Stochastics Probability & Statistics Calculus & Mathematical Analysis Differential Calculus & Equations

Other Editions and Formats

Hardcover

Published: 13th March 1995

View Product

Existence and uniqueness for diffusion processes
The basic properties of diffusion processes
The spectral theory of elliptic operators on smooth bounded domains
Generalized spectral theory for operators on arbitrary domains
Applications to the one-dimensional case and the radially symmetric multi-dimensional case
Criteria for transience or recurrence and explosion or non-explosion of diffusion processes
Positive harmonic functions and the Martin boundary: general theory
Positive harmonic functions and the Martin boundary: applications to certain classes of operators
Bounded harmonic functions and applications to Brownian motion and the Laplacian on a manifold of non-positive curvature
Table of Contents provided by Publisher. All Rights Reserved.

Positive Harmonic Functions and Diffusion

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

More in Stochastics

Stochastic Control in Energy, Environmental and Resource Management Applications

Emerging Methodologies and Applications in Modelling, Identification and Control

Introduction to Stochastic Processes

2nd Edition

Introduction to Probability

2nd edition

Backward Stochastic Volterra Integral Equations

Probability Theory and Stochastic Modelling

Markov Chain Monte Carlo

Stochastic Simulation for Bayesian Inference

Markov Chain Monte Carlo

Stochastic Simulation for Bayesian Inference

Stochastic Navier-Stokes Equations on Spheres and Spherical Shells

Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

Logistic Regression

Bridging Theory and Practice

Copula Models for Dependent Competing Risks

Theory and applications in economics, engineering and medicine

Occupancy Estimation and Modeling

Inferring Patterns and Dynamics of Species Occurrence

Introduction To Stochastic Calculus With Applications (Third Edition)

Mathematics of Epidemics on Networks

From Exact to Approximate Models

Understanding Markov Chains

Examples and Applications

Information Theory, Probability and Statistical Learning

A Festschrift in Honor of Andrew Barron

From Classical Analysis to Analysis on Fractals

A Tribute to Robert Strichartz, Volume 2

Optimal Control in Random Environments

Pontryagin Maximum Principle with Environment-dependent Jumps and Mean-Field Games with Common Poissonian Noise

A Course of Stochastic Analysis

CMS/CAIMS Books in Mathematics

Models for Longitudinal Data with Applications to Early Warning Systems

Workshops of the PRIN Project, Perugia, Italy, 19 September 2024, 11 September 2025 and 23 January 2026

Analysis and Geometry of Random Fields

Springer INdAM Series

Approximations to Probabilistic Characteristics of Stochastic Differential Equations

Lecture Notes in Mathematics

Branching Processes and Related Fields

Lecture Notes in Statistics

Applied Stochastic Modeling

Synthesis Lectures on Mathematics & Statistics

Mathematical Structures I—Stochastic and Analytic Structures with Applications

Exploring the World of Mathematical Structures Workshop, Vasteras, Sweden, May 14-16, 2024

Exploring Information Geometry

Recent Advances and Connections to Topological Field Theory

This product is categorised by