Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal Inequalities and Some Applications   A maximal inequality is an inequality which involves the (absolute) supremum
$\sup_{s\leq t}|X_{s}|$ or the running maximum $\sup_{s\leq t}X_{s}$ of a
stochastic process $(X_t)_{t\geq 0}$. We discuss maximal inequalities for
several classes of stochastic processes with values in an Euclidean space:
Martingales, L\'evy processes, L\'evy-type - including Feller processes,
(compound) pseudo Poisson processes, stable-like processes and solutions to
SDEs driven by a L\'evy process -, strong Markov processes and Gaussian
processes. Using the Burkholder-Davis-Gundy inequalities we als discuss some
relations between maximal estimates in probability and the Hardy-Littlewood
maximal functions from analysis.

7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol