Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A relatively short proof of It\^o's formula for SPDEs and its
  applications   We give a short proof of It\^o's formula for stochastic Hilbert-space valued
processes in the setting $V\subset H\subset V^{*}$ based on the possibility to
lift the stochastic differentials, which are originally in $V^{*}$, into $H$.
Using this result we also prove the maximum principle for second-order SPDEs in
arbitrary domains.

25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs