Direct solution of a Riccati equation arising in stochastic control theory
The main result of the paper is that of existence and uniqueness for the Riccati equation, which arises in the solution of an abstract linear stochastic optimal control problem with a quadratic cost functional; the system is posed on a Hilbert space and the system operator and the noise operator are both unbounded. The solution to the control problem then follows by the usual dynamic programming arguments [\textit{A. Ichikawa}, SIAM J. Control Optimization 17, 152-174 (1979; Zbl 0434.93069)].
scientific article; zbMATH DE number 3885779