Critical Brownian sheet does not have double points
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- dc.contributor.author Dalang, Robert C.ca
- dc.contributor.author Khoshnevisan, Davarca
- dc.contributor.author Nualart, Eulàliaca
- dc.contributor.author Wu, Dongshengca
- dc.contributor.author Xiao, Yiminca
- dc.date.accessioned 2018-04-18T08:31:18Z
- dc.date.available 2018-04-18T08:31:18Z
- dc.date.issued 2012
- dc.description.abstract We derive a decoupling formula for the Brownian sheet which has the following ready consequence: An N-parameter Brownian sheet in Rd has double points if and only if d<4N. In particular, in the critical case where d=4N, the Brownian sheet does not have double points. This answers an old problem in the folklore of the subject. We also discuss some of the geometric consequences of the mentioned decoupling, and establish a partial result concerning k-multiple points in the critical case k(d−2N)=d.en
- dc.description.sponsorship Dalang RC is supported by grant from the Swiss National Science Foundation. Khoshnevisan D and Xiao Y are supported by grant from the US National Science Foundation.
- dc.format.mimetype application/pdf
- dc.identifier.citation Dalang RC, Khoshnevisan D, Nualart E, Wu D, Xiao Y. Critical Brownian sheet does not have double points. Ann Probab. 2012;40(4):1829-59. DOI: 10.1214/11-AOP665
- dc.identifier.doi http://dx.doi.org/10.1214/11-AOP665
- dc.identifier.issn 0091-1798
- dc.identifier.uri http://hdl.handle.net/10230/34391
- dc.language.iso eng
- dc.publisher Institute of Mathematical Statistics (IMS)ca
- dc.relation.ispartof The Annals of Probability. 2012;40(4):1829-59.
- dc.rights © Institute of Mathematical Statistics, 2012
- dc.rights.accessRights info:eu-repo/semantics/openAccess
- dc.subject.keyword Brownian sheeten
- dc.subject.keyword Multiple pointsen
- dc.subject.keyword Capacityen
- dc.subject.keyword Hausdorff dimensionen
- dc.title Critical Brownian sheet does not have double pointsca
- dc.type info:eu-repo/semantics/article
- dc.type.version info:eu-repo/semantics/publishedVersion