Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Expected uniform integration approximation under general equal measure
  partition   In this paper, we study bounds of expected $L_2-$discrepancy to give mean
square error of uniform integration approximation for functions in Sobolev
space $\mathcal{H}^{\mathbf{1}}(K)$, where $\mathcal{H}$ is a reproducing
Hilbert space with kernel $K$. Better order $O(N^{-1-\frac{1}{d}})$ of
approximation error is obtained, comparing with previously known rate
$O(N^{-1})$ using crude Monte Carlo method. Secondly, we use expected
$L_{p}-$discrepancy bound($p\ge 1$) of stratified samples to give several upper
bounds of $p$-moment of integral approximation error in general Sobolev space
$F_{d,q}^{*}$.

22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
4
The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph