## Bernoulli

• Bernoulli
• Volume 16, Number 4 (2010), 926-952.

### Hausdorff and packing dimensions of the images of random fields

#### Abstract

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.

#### Article information

Source
Bernoulli, Volume 16, Number 4 (2010), 926-952.

Dates
First available in Project Euclid: 18 November 2010

https://projecteuclid.org/euclid.bj/1290092890

Digital Object Identifier
doi:10.3150/09-BEJ244

Mathematical Reviews number (MathSciNet)
MR2759163

Zentralblatt MATH identifier
1227.60049

#### Citation

Shieh, Narn-Rueih; Xiao, Yimin. Hausdorff and packing dimensions of the images of random fields. Bernoulli 16 (2010), no. 4, 926--952. doi:10.3150/09-BEJ244. https://projecteuclid.org/euclid.bj/1290092890

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