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Positive harmonic functions and diff...

Pinsky, Ross, G.

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Positive harmonic functions and diffusion

Record Type:	Electronic resources : Monograph/item
Title/Author:	Positive harmonic functions and diffusion/ Ross G. Pinsky.
remainder title:	Positive Harmonic Functions & Diffusion
Author:	Pinsky, Ross, G.
Published:	Cambridge :Cambridge University Press, : 1995.,
Description:	xvi, 474 p. :ill., digital ;24 cm.
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Diffusion processes. -
Online resource:	https://doi.org/10.1017/CBO9780511526244
ISBN:	9780511526244

Positive harmonic functions and diffusion
Pinsky, Ross, G.

Positive harmonic functions and diffusion[electronic resource] /Positive Harmonic Functions & DiffusionRoss G. Pinsky. - Cambridge :Cambridge University Press,1995. - xvi, 474 p. :ill., digital ;24 cm. - Cambridge studies in advanced mathematics ;45. - Cambridge studies in advanced mathematics ;45..

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

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.

ISBN: 9780511526244Subjects--Topical Terms:

648159
Diffusion processes.

LC Class. No.: QA274.75 / .P56 1995

Dewey Class. No.: 519.233

Positive harmonic functions and diffusion
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245 1 0 $a Positive harmonic functions and diffusion $h [electronic resource] / $c Ross G. Pinsky.
246 3 $a Positive Harmonic Functions & Diffusion
260 $a Cambridge : $b Cambridge University Press, $c 1995.
300 $a xvi, 474 p. : $b ill., digital ; $c 24 cm.
490 1 $a Cambridge studies in advanced mathematics ; $v 45
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
520 $a 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.
650 0 $a Diffusion processes. $3 648159
650 0 $a Elliptic operators. $3 555715
830 0 $a Cambridge studies in advanced mathematics ; $v 45. $3 3470567
856 4 0 $u https://doi.org/10.1017/CBO9780511526244