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In this paper, we consider a class of general linear forward and backward stochastic difference equations (FBSDEs) which are fully coupled. The necessary and sufficient condition for the existence of a unique solution to FBSDEs is given in terms of a Riccati equation. The result is applied to the linear quadratic optimal control problem for systems with stochastic multiplicative noises.
In this paper, we study the stochastic linear quadratic regulation problem for linear discrete-time systems with multiple input channels. A necessary and sufficient condition is obtained by applying the leader-follower game approach. Different from the augmentation technique, the complete solution is given in terms of one difference Riccati equation and one Riccati-type equation. The key is to introduce...
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