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...
| Autores: | , |
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| 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 |
| 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. |
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