Abstract

We consider a nonlinear filtering problem of multiscale non-Gaussian signal processes and observation processes with jumps. First, we prove that the dimension for the signal system can be reduced by a homogenized approach. Second, convergence of the corresponding nonlinear filtering to the homogenized filtering is shown by a weak convergence technique. Finally, we give an example to explain our result.

中文翻译：

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具有Lévy噪声的随机动力系统的非线性滤波的收敛性

摘要

我们考虑了多尺度非高斯信号过程和具有跳跃现象的观测过程的非线性滤波问题。首先，我们证明了信号系统的尺寸可以通过均匀化方法来减小。其次，通过弱收敛技术显示了对应的非线性滤波到均质滤波的收敛。最后，我们举一个例子来说明我们的结果。