Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic Programming Principle for Backward Doubly Stochastic Recursive
  Optimal Control Problem and Sobolev Weak Solution of The Stochastic
  Hamilton-Bellman Equation   In this paper, we study backward doubly stochastic recursive optimal control
problem where the cost function is described by the solution of a backward
doubly stochastic differential equation. We give the dynamical programming
principle for this kind of optimal control problem and show that the value
function is the unique Sobolev weak solution for the corresponding stochastic
Hamilton-Jacobi-Bellman equation.

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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org