NDLI: 3G-inequality for planar domains

Content Provider	Springer Nature Link
Author	Hansen, Wolfhard
Copyright Year	2011
Abstract	The 3G-inequality for Green functions g D on arbitrary bounded domains in $${{\mathbb{R}}^2}$$ , which Bass and Burdzy (Probab Theory Relat Fields 101(4):479–493, 1995) obtained by a genuinely probabilistic proof (using loops of Brownian motion around the origin), is proven (in a more precise form) employing elementary properties of harmonic measures only. Since harmonic measures are hitting distributions of Brownian motion, this purely analytic proof can be viewed as well as being probabilistic. A spin-off is an upper estimate of g D on subdisks B′ of an open disk B in terms of g B divided by the capacity of $${B'\setminus D}$$ with respect to B.
Ending Page	366
Page Count	10
Starting Page	357
File Format	PDF
ISSN	01788051
e-ISSN	14322064
Journal	Probability Theory and Related Fields
Issue Number	1
Volume Number	152
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-11-03
Publisher Place	Berlin/Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Loop Planar domain Greenian domain Mathematical and Computational Biology Theoretical, Mathematical and Computational Physics Harmonic measure Probability Theory and Stochastic Processes Potentials and capacity, harmonic measure, extremal length Green function Probabilistic potential theory Quantitative Finance Brownian motion Capacity Statistics for Business/Economics/Mathematical Finance/Insurance Operations Research/Decision Theory 3G-inequality
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Analysis Statistics, Probability and Uncertainty

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