Wonham滤波器稳定性的对偶刻画
A Dual Characterization of the Stability of the Wonham Filter
摘要：
本文重新讨论了非线性Wonham滤波器稳定性的经典问题。本文的新贡献是两方面的：（一）定义的（控制理论）对偶的非线性滤波的稳定性;和（ii）使用这个定义，以获得结论的稳定性的Wonham滤波器。具体而言，它示出的对偶系统的可镇定性是必要的过滤器的稳定性和相反的可镇定性意味着过滤器渐近检测正确的遍历类。的制定和证明是基于最近发现的对偶结果，即非线性滤波问题是作为一个随机最优控制问题的向后随机微分方程（BENDE）。控制理论证明技术和结果可以看作是一个推广的经典工作的稳定性卡尔曼滤波器。
英文摘要：
This paper revisits the classical question of the stability of the nonlinear Wonham filter. The novel contributions of this paper are two-fold: (i) definition of the stabilizability for the (control-theoretic) dual to the nonlinear filter; and (ii) the use of this definition to obtain conclusions on the stability of the Wonham filter. Specifically, it is shown that the stabilizability of the dual system is necessary for filter stability and conversely stabilizability implies that the filter asymptotically detects the correct ergodic class. The formulation and the proofs are based upon a recently discovered duality result whereby the nonlinear filtering problem is cast as a stochastic optimal control problem for a backward stochastic differential equation (BSDE). The control-theoretic proof techniques and results may be viewed as a generalization of the classical work on the stability of the Kalman filter.
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