Bernoulli

  • Bernoulli
  • Volume 14, Number 3 (2008), 865-898.

Local times of multifractional Brownian sheets

Mark Meerschaert, Dongsheng Wu, and Yimin Xiao

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Abstract

Denote by $H(t)=(H_1(t), …, H_N(t))$ 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.

Article information

Source
Bernoulli, Volume 14, Number 3 (2008), 865-898.

Dates
First available in Project Euclid: 25 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.bj/1219669633

Digital Object Identifier
doi:10.3150/08-BEJ126

Mathematical Reviews number (MathSciNet)
MR2537815

Zentralblatt MATH identifier
1186.60036

Keywords
Hausdorff dimension level sets local times multifractional Brownian sheets one-sided sectorial local non-determinism

Citation

Meerschaert, Mark; Wu, Dongsheng; Xiao, Yimin. Local times of multifractional Brownian sheets. Bernoulli 14 (2008), no. 3, 865--898. doi:10.3150/08-BEJ126. https://projecteuclid.org/euclid.bj/1219669633


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