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DCDS-B

Some stochastic optimal control problems in a Hilbert space are
formulated and solved. The controlled equations are abstract
equations in a HIlbert space that can model stochastic partial
differential equations and stochastic delay equations. Both linear
and semilinear equations are considered where the cylindrical
Brownian motion can occur as distributed, boundary, or at discrete
points in the domain. For the linear equations, the cost is an
ergodic, quadratic functional of the state and the control. An
optimal linear feedback control is given explicitly. For the
semilinear equations, the cost is an ergodic functional. Some
results for the null controllability of a stochastic parabolic
equation are given. A control problem for a finite dimension linear
stochastic system with an arbitrary fractional Brownian motion and a
quadratic cost functional is formulated and explicitly solved.

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