Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wavelet Series Representation and Geometric Properties of Harmonizable
  Fractional Stable Sheets   Let $Z^H= \{Z^H(t), t \in \R^N\}$ be a real-valued $N$-parameter harmonizable
fractional stable sheet with index $H = (H_1, \ldots, H_N) \in (0, 1)^N$. We
establish a random wavelet series expansion for $Z^H$ which is almost surely
convergent in all the H\"older spaces $C^\gamma ([-M,M]^N)$, where $M>0$ and
$\gamma\in (0, \min\{H_1,\ldots, H_N\})$ are arbitrary. One of the main
ingredients for proving the latter result is the LePage representation for a
rotationally invariant stable random measure.
  Also, let $X=\{X(t), t \in \R^N\}$ be an $\R^d$-valued harmonizable
fractional stable sheet whose components are independent copies of $Z^H$. By
making essential use of the regularity of its local times, we prove that, on an
event of positive probability, the formula for the Hausdorff dimension of the
inverse image $X^{-1}(F)$ holds for all Borel sets $F \subseteq \R^d$. This is
referred to as a uniform Hausdorff dimension result for the inverse images.

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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: physics
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The categories of this paper are: nucl-th
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The categories of this paper are: cs
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: mtrl-th