Local times of multifractional Brownian sheets
نویسنده
چکیده
Denote by H(t) = (H1(t), . . . ,HN (t)) a function in t ∈ R+ with values in (0, 1) . Let {B(t)} = {B(t), t ∈ R+} 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(t)}. We also determine the Hausdorff dimensions of the level sets of {B(t)}. Our results extend the corresponding results for fractional Brownian sheets and multifractional Brownian motion to multifractional Brownian sheets. Running head: Local times of multifractional Brownian sheets 2000 AMS Classification numbers: 60G15, 60G17; 42C40; 28A80.
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تاریخ انتشار 2007