Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bounds for stochastic processes on product index spaces   In this paper we discuss the question how to bound supremum of a stochastic
process with the index set of a product type. There is a tempting idea to
approach the question by the analysis of the process on each of the marginal
index spaces separately. However it turns out that we also need to study
suitable partitions of the whole index space. We show what can be done in this
direction and how to use the method to reprove some known results. In
particular we observe that all known applications of the Bernoulli Theorem can
be obtained in this way, moreover we use the shattering dimension to slightly
extend the application to VC classes. We also show some application to the
regularity of paths for processes which take values in vector spaces. Finally
we give a short proof of the Mendelson-Paouris result on sums of squares for
empirical processes.

31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom