Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A remark on the rates of convergence for integrated volatility
  estimation in the presence of jumps   The optimal rate of convergence of estimators of the integrated volatility,
for a discontinuous It\^{o} semimartingale sampled at regularly spaced times
and over a fixed time interval, has been a long-standing problem, at least when
the jumps are not summable. In this paper, we study this optimal rate, in the
minimax sense and for appropriate "bounded" nonparametric classes of
semimartingales. We show that, if the $r$th powers of the jumps are summable
for some $r\in[0,2)$, the minimax rate is equal to $\min(\sqrt{n},(n\log
n)^{(2-r)/2})$, where $n$ is the number of observations.

9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc