Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal generalization of Baum-Katz theorem and optimality of sequential
  tests   Baum-Katz theorem asserts that the Cesaro means of i.i.d. increments
distributed like X r-converge if and only if |X|^{r+1} is integrable. We
generalize this, and we unify other results, by proving that the following
equivalence holds, if and only if G is moderate: the Cesaro means G-converge if
and only if G(L(a)) is integrable for every a if and only if |X|.G(|X|) is
integrable. Here, L(a) is the last time when the deviation of the Cesaro mean
from its limit exceeds a, and G-convergence is the analogue of r-convergence.
This solves a question about the asymptotic optimality of Wald's sequential
tests.

27
The categories of this paper are: comp-gas
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat
21
The categories of this paper are: adap-org
22
The categories of this paper are: chao-dyn