Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derivative Formula and Applications for Degenerate Diffusion Semigroups   By using the Malliavin calculus and solving a control problem, Bismut type
derivative formulae are established for a class of degenerate diffusion
semigroups with non-linear drifts. As applications, explicit gradient estimates
and Harnack inequalities are derived.

5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin