Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convergence of random series and the rate of convergence of the strong
  law of large numbers in game-theoretic probability   We give a unified treatment of the convergence of random series and the rate
of convergence of strong law of large numbers in the framework of
game-theoretic probability of Shafer and Vovk (2001). We consider games with
the quadratic hedge as well as more general weaker hedges. The latter
corresponds to existence of an absolute moment of order smaller than two in the
measure-theoretic framework. We prove some precise relations between the
convergence of centered random series and the convergence of the series of
prices of the hedges. When interpreted in measure-theoretic framework, these
results characterize convergence of a martingale in terms of convergence of the
series of conditional absolute moments. In order to prove these results we
derive some fundamental results on deterministic strategies of Reality, who is
a player in a protocol of game-theoretic probability. It is of particular
interest, since Reality's strategies do not have any counterparts in
measure-theoretic framework, ant yet they can be used to prove results, which
can be interpreted in measure-theoretic framework.

15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org