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dc.contributor.authorJiang, Jianping
dc.contributor.authorKennedy, Tom
dc.date.accessioned2018-05-30T22:07:36Z
dc.date.available2018-05-30T22:07:36Z
dc.date.issued2017-12
dc.identifier.citationJiang, J. & Kennedy, T. J Theor Probab (2017) 30: 1424. https://doi.org/10.1007/s10959-016-0695-3en_US
dc.identifier.issn0894-9840
dc.identifier.issn1572-9230
dc.identifier.doi10.1007/s10959-016-0695-3
dc.identifier.urihttp://hdl.handle.net/10150/627847
dc.description.abstractWe consider a discrete-time, continuous-state random walk with steps uniformly distributed in a disk of radius h. For a simply connected domain D in the plane, let omega(h)(0, .; D) be the discrete harmonic measure at 0 is an element of D associated with this random walk, and omega(0, .; D) be the (continuous) harmonic measure at 0. For domains D with analytic boundary, we prove there is a bounded continuous function sigma(D)(z) on partial derivative D such that for functions g which are in C2+sigma (partial derivative D) for some alpha > 0 we have lim(h down arrow 0) integral(partial derivative D) g(xi)omega(h)( 0, vertical bar d xi vertical bar; D) - integral(partial derivative D) g(xi)omega(0, vertical bar d xi vertical bar; D)/h = integral(partial derivative D) g(z)sigma(D)(z)vertical bar dz vertical bar. We give an explicit formula for sigma(D) in terms of the conformal map from D to the unit disk. The proof relies on some fine approximations of the potential kernel and Green's function of the random walk by their continuous counterparts, which may be of independent interest.en_US
dc.description.sponsorshipNSF [DMS-1500850]en_US
dc.language.isoenen_US
dc.publisherSPRINGER/PLENUM PUBLISHERSen_US
dc.relation.urlhttp://link.springer.com/10.1007/s10959-016-0695-3en_US
dc.rights© Springer Science+Business Media New York 2016en_US
dc.subjectRandom walken_US
dc.subjectBrownian motionen_US
dc.subjectHarmonic measureen_US
dc.subjectDirichlet problemen_US
dc.titleThe Difference Between a Discrete and Continuous Harmonic Measureen_US
dc.typeArticleen_US
dc.contributor.departmentUniv Arizona, Dept Mathen_US
dc.identifier.journalJOURNAL OF THEORETICAL PROBABILITYen_US
dc.description.note12 month embargo; published online: 07 June 2016en_US
dc.description.collectioninformationThis item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.en_US
dc.eprint.versionFinal accepted manuscripten_US
dc.source.journaltitleJournal of Theoretical Probability
dc.source.volume30
dc.source.issue4
dc.source.beginpage1424
dc.source.endpage1444
refterms.dateFOA2017-06-07T00:00:00Z


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