Level sets of multiparameter Brownian motions

We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2(loglog(1r))d/2 is the exact Hausdorff measure function for the zero level set of an N-parameter d-dimensional additive Brownian motion. We extend this result to a natural multiparameter vers...

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Detalles Bibliográficos
Autores: Nualart, Eulàlia, Mountford, Thomas S.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2004
País:España
Institución:Universitat Pompeu Fabra
Repositorio:Repositorio Digital de la UPF
OAI Identifier:oai:repositori.upf.edu:10230/34388
Acceso en línea:http://hdl.handle.net/10230/34388
http://dx.doi.org/10.1214/EJP.v9-169
Access Level:acceso abierto
Palabra clave:Local times
Hausdorff measure
Level sets
Additive Brownian motion
Descripción
Sumario:We use Girsanov's theorem to establish a conjecture of Khoshnevisan, Xiao and Zhong that ϕ(r)=rN−d/2(loglog(1r))d/2 is the exact Hausdorff measure function for the zero level set of an N-parameter d-dimensional additive Brownian motion. We extend this result to a natural multiparameter version of Taylor and Wendel's theorem on the relationship between Brownian local time and the Hausdorff ϕ-measure of the zero set.