Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A nonlinear Bismut-Elworthy formula for HJB equations with quadratic
  Hamiltonian in Banach spaces   We consider a Backward Stochastic Differential Equation (BSDE for short) in a
Markovian framework for the pair of processes $(Y,Z)$, with generator with
quadratic growth with respect to $Z$. The forward equation is an evolution
equation in an abstract Banach space. We prove an analogue of the
Bismut-Elworty formula when the diffusion operator has a pseudo-inverse not
necessarily bounded and when the generator has quadratic growth with respect to
$Z$. In particular, our model covers the case of the heat equation in space
dimension greater than or equal to 2. We apply these results to solve
semilinear Kolmogorov equations for the unknown $v$, with nonlinear term with
quadratic growth with respect to $\nabla v$ and final condition only bounded
and continuous, and to solve stochastic optimal control problems with quadratic
growth.

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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: econ