Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First and second order necessary conditions for stochastic optimal
  controls   The main purpose of this paper is to establish the first and second order
necessary optimality conditions for stochastic optimal controls using the
classical variational analysis approach. The control system is governed by a
stochastic differential equation, in which both drift and diffusion terms may
contain the control variable and the set of controls is allowed to be
nonconvex. Only one adjoint equation is introduced to derive the first order
necessary condition; while only two adjoint equations are needed to state the
second order necessary conditions for stochastic optimal controls.

3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin