Packing-dimension profiles and fractional Brownian motion

• Autores: Davar Khoshnevisan, Yimin Xiao
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 145, Nº 1, 2008, págs. 205-214
• Idioma: inglés
• DOI: 10.1017/s0305004108001394
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• Resumen

  • In order to compute the packing dimension of orthogonal projections Falconer and Howroyd [3] have introduced a family of packing dimension profiles Dims that are parametrized by real numbers s > 0. Subsequently, Howroyd [5] introduced alternate s-dimensional packing dimension profiles P-Dims by using Caratheodory-type packing measures, and proved, among many other things, that P-Dims E = Dims E for all integers s > 0 and all analytic sets E RN.

    The aim of this paper is to prove that P-Dims E = Dims E for all real numbers s > 0 and analytic sets E RN. This answers a question of Howroyd [5, p. 159]. Our proof hinges on establishing a new property of fractional Brownian motion