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DCDS-B

We derive a large deviation principle for a stochastic Navier-Stokes equation
for the vorticity of a two-dimensional fluid when the magnitude of the random term tends
to zero. The key is the verification of the exponential tightness for the
stochastic vorticity.

MCRF

In this paper, we study the generalized mean-field stochastic control problem when the usual stochastic maximum principle (SMP) is not applicable due to the singularity of the Hamiltonian function. In this case, we derive a second order SMP. We introduce the adjoint process by the generalized mean-field backward stochastic differential equation. The keys in the proofs are the expansion of the cost functional in terms of a perturbation parameter, and the use of the range theorem for vector-valued measures.

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