Local times of multifractional Brownian sheets

2008/10/24 by Mark Meerschaert, Dongsheng Wu, Yimin Xiao · 1 citation
Mathematics · #math.PR #math.ST #stat.TH

paper · pdf · doi:10.3150/08-bej126

published as Bernoulli 2008, Vol. 14, No. 3, 865-898 · Published in at http://dx.doi.org/10.3150/08-BEJ126 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)

arxiv created 2008/10/24 · arxiv updated 2009/12/01

Abstract

Denote by H(t)=(H₁(t),...,H_N(t)) a function in t∈ℝ₊^N with values in (0,1)^N. Let \B^H(t)(t)\=\B^H(t)(t),t∈ℝ^N₊\ be an (N,d)-multifractional Brownian sheet (mfBs) with Hurst functional H(t). Under some regularity conditions on the function H(t), we prove the existence, joint continuity and the Hölder regularity of the local times of \B^H(t)(t)\. We also determine the Hausdorff dimensions of the level sets of \B^H(t)(t)\. Our results extend the corresponding results for fractional Brownian sheets and multifractional Brownian motion to multifractional Brownian sheets.

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