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The Partially Observed Stochastic Minimum Principle.
Various proofs have been given of the minimum principle satisfied by an optimal control in a partially observed stochastic control problem. See, for example, the papers by Bensoussan , Elliott , Haussmann , and ...
The Conditional Adjoint Process.
The adjoint and minimum principle for a partially observed diffusion can be obtained by differentiating the statement that a control u* is optimal. Using stochastic flows the variation in the cost resulting from a change ...