64,295 research outputs found
A Maximum Principle for Optimal Control of Stochastic Evolution Equations
A general maximum principle is proved for optimal controls of abstract
semilinear stochastic evolution equations. The control variable, as well as
linear unbounded operators, acts in both drift and diffusion terms, and the
control set need not be convex.Comment: 20 page
On backward stochastic evolution equations in Hilbert space and optimal control
In this paper a new result on the existence and uniqueness of the adapted solution to a backward stochastic evolution equation in Hilbert spaces under non Lipschitz condition is established. The applicability of this result is then illustrated in a discussion of some concrete backward stochastic partial differential equation. Furthermore, stochastic maximum principle for optimal control problems of stochastic systems governed by backward stochastic evolution equations in Hilbert spaces is obtained
Maximum principle for optimal control of stochastic evolution equations with recursive utilities
We consider the optimal control problem of stochastic evolution equations in
a Hilbert space under a recursive utility, which is described as the solution
of a backward stochastic differential equation (BSDE). A very general maximum
principle is given for the optimal control, allowing the control domain not to
be convex and the generator of the BSDE to vary with the second unknown
variable . The associated second-order adjoint process is characterized as a
unique solution of a conditionally expected operator-valued backward stochastic
integral equation
Stochastic maximum principle for SPDEs with delay.
In this paper we develop necessary conditions for optimality, in the form of
the Pontryagin maximum principle, for the optimal control problem of a class of
infinite dimensional evolution equations with delay in the state. In the cost
functional we allow the final cost to depend on the history of the state. To
treat such kind of cost functionals we introduce a new form of anticipated
backward stochastic differential equations which plays the role of dual
equation associated to the control problem
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