Open Access
November 2010 Hausdorff and packing dimensions of the images of random fields
Narn-Rueih Shieh, Yimin Xiao
Bernoulli 16(4): 926-952 (November 2010). DOI: 10.3150/09-BEJ244


Let $X = \{X(t), t ∈ ℝ^N\}$ be a random field with values in $ℝ^d$. For any finite Borel measure $μ$ and analytic set $E ⊂ ℝ^N$, the Hausdorff and packing dimensions of the image measure $μ_X$ and image set $X(E)$ are determined under certain mild conditions. These results are applicable to Gaussian random fields, self-similar stable random fields with stationary increments, real harmonizable fractional Lévy fields and the Rosenblatt process.


Download Citation

Narn-Rueih Shieh. Yimin Xiao. "Hausdorff and packing dimensions of the images of random fields." Bernoulli 16 (4) 926 - 952, November 2010.


Published: November 2010
First available in Project Euclid: 18 November 2010

zbMATH: 1227.60049
MathSciNet: MR2759163
Digital Object Identifier: 10.3150/09-BEJ244

Keywords: Hausdorff dimension , images , Packing dimension , packing dimension profiles , real harmonizable fractional Lévy motion , Rosenblatt process , self-similar stable random fields

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

Vol.16 • No. 4 • November 2010
Back to Top