无限时域有限状态非线性滤波的模型鲁棒性
Model robustness of finite state nonlinear filtering over the infinite time horizon
摘要：
研究了在白噪声中观测到的连续时间有限状态马尔可夫链的非线性滤波对模型参数误设定的鲁棒性。它示出的最优滤波器和不正确的模型参数之间的距离收敛到零均匀在无限的时间间隔上的误指定的模型收敛到真正的模型，提供的信号服从混合条件。通过非线性滤波的导数相对于其初始条件的指数衰减来控制滤波误差。我们允许同时误指定的初始条件，信号的过渡率，和观察功能。前两种情况下处理的相对初级的手段，而后者的情况下，需要使用Skorokhod积分和工具的预期随机分析。
英文摘要：
We investigate the robustness of nonlinear filtering for continuous time finite state Markov chains, observed in white noise, with respect to misspecification of the model parameters. It is shown that the distance between the optimal filter and that with incorrect model parameters converges to zero uniformly over the infinite time interval as the misspecified model converges to the true model, provided the signal obeys a mixing condition. The filtering error is controlled through the exponential decay of the derivative of the nonlinear filter with respect to its initial condition. We allow simultaneously for misspecification of the initial condition, of the transition rates of the signal, and of the observation function. The first two cases are treated by relatively elementary means, while the latter case requires the use of Skorokhod integrals and tools of anticipative stochastic calculus.
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