Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum principle for optimal control of stochastic partial differential
  equations   We shall consider a stochastic maximum principle of optimal control for a
control problem associated with a stochastic partial differential equations of
the following type:
  d x(t) = (A(t) x(t) + a (t, u(t)) x(t) + b(t, u(t)) dt + [<\sigma(t, u(t)),
x(t)>_K + g (t, u(t))] dM(t),
  x(0) = x_0 \in K,
  with some given predictable mappings $a, b, \sigma, g$ and a continuous
martingale $M$ taking its values in a Hilbert space $K,$ while $u(\cdot)$
represents a control. The equation is also driven by a random unbounded linear
operator $A(t,w), \; t \in [0,T ], $ on $K .$ We shall derive necessary
conditions of optimality for this control problem without a convexity
assumption on the control domain, where $u(\cdot)$ lives, and also when this
control variable is allowed to enter in the martingale part of the equation.

22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ