Quadrature domains and Brownian motion - (A heuristic approach)
2005 (English)In: Quadrature Domains and Their Applications: The Harold S. Shapiro Anniversary Volume / [ed] Ebenfelt, P; Gaustafsson, B; Khavinson, D; Putinar, M, 2005, Vol. 156, 207-215 p.Conference paper (Refereed)
In this note we will make an attempt to link the theory of the so-called quadrature domains (QD) to stochastic analysis. We show that a QD, with the underlying measure M, can be represented as the set of points x, for which the expectation value (average reward) E-x (-theta + integral(theta)(0) mu(X-t)), is positive for some (bounded) stopping time theta. Here X-t denotes the Brownian motion starting at the point x, and E-x denotes the expectation with respect to the underlying probability measure P-x.
Place, publisher, year, edition, pages
2005. Vol. 156, 207-215 p.
, OPERATOR THEORY : ADVANCES AND APPLICATIONS, ISSN 0255-0156 ; 156
Brownian motion, quadrature domains, variational inequalities
IdentifiersURN: urn:nbn:se:kth:diva-43268ISI: 000228460400011ISBN: 3-7643-7145-5OAI: oai:DiVA.org:kth-43268DiVA: diva2:448729
Conference on Quadrature Domains and Their Applications held in honor of Harold S Shapiro 75th Birthday Location: Univ Calif Santa Barbara, Santa Barbara, CA Date: MAR 27-30, 2003
QC 201110182011-10-182011-10-142011-10-18Bibliographically approved