Kalman-Bucy filtering equations of forward and backward stochastic systems and applications to recursive optimal control problems |
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Authors: | Guangchen Wang Zhen Wu |
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Institution: | a School of Mathematical Sciences, Shandong Normal University, Jinan 250014, PR China b School of Mathematics and System Sciences, Shandong University, Jinan 250100, PR China |
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Abstract: | This paper is concerned with Kalman-Bucy filtering problems of a forward and backward stochastic system which is a Hamiltonian system arising from a stochastic optimal control problem. There are two main contributions worthy pointing out. One is that we obtain the Kalman-Bucy filtering equation of a forward and backward stochastic system and study a kind of stability of the aforementioned filtering equation. The other is that we develop a backward separation technique, which is different to Wonham's separation theorem, to study a partially observed recursive optimal control problem. This new technique can also cover some more general situation such as a partially observed linear quadratic non-zero sum differential game problem is solved by it. We also give a simple formula to estimate the information value which is the difference of the optimal cost functionals between the partial and the full observable information cases. |
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Keywords: | Backward stochastic differential equation Feynman-Kac formula Kalman-Bucy filtering Linear quadratic non-zero sum differential game Recursive optimal control Stability |
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