Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Path regularity of Brownian motion and Brownian sheet   By the work of P. L\'evy, the sample paths of the Brownian motion are known
to satisfy a certain H\"older regularity condition almost surely. This was
later improved by Ciesielski, who studied the regularity of these paths in
Besov and Besov-Orlicz spaces. We review these results and propose new function
spaces of Besov type, strictly smaller than those of Ciesielski and L\'evy,
where the sample paths of the Brownian motion lie in almost surely. In the same
spirit, we review and extend the work of Kamont, who investigated the same
question for the multivariate Brownian sheet and function spaces of dominating
mixed smoothness.

28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn