Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The $b$-adic tent transformation for quasi-Monte Carlo integration using
  digital nets   In this paper we investigate quasi-Monte Carlo (QMC) integration using
digital nets over $\mathbb{Z}_b$ in reproducing kernel Hilbert spaces. The tent
transformation, or the baker's transformation, was originally used for lattice
rules by Hickernell (2002) to achieve higher order convergence of the
integration error for smooth non-periodic integrands, and later, has been
successfully applied to digital nets over $\mathbb{Z}_2$ by Cristea et al.
(2007) and Goda (2014). The aim of this paper is to generalize the latter two
results to digital nets over $\mathbb{Z}_b$ for an arbitrary prime $b$. For
this purpose, we introduce the {\em $b$-adic tent transformation} for an
arbitrary positive integer $b$ greater than 1, which is a generalization of the
original (dyadic) tent transformation. Further, again for an arbitrary positive
integer $b$ greater than 1, we analyze the mean square worst-case error of QMC
rules using digital nets over $\mathbb{Z}_b$ which are randomly digitally
shifted and then folded using the $b$-adic tent transformation in reproducing
kernel Hilbert spaces. Using this result, for a prime $b$, we prove the
existence of good higher order polynomial lattice rules over $\mathbb{Z}_b$
among the smaller number of candidates as compared to the result by Dick and
Pillichshammer (2007), which achieve almost the optimal convergence rate of the
mean square worst-case error in unanchored Sobolev spaces of smoothness of
arbitrary high order.

12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat