Convergence of nonlinear filterings for stochastic dynamical systems with Lévy noises

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.

Keywords:

• Nonlinear filtering
• dimensional reduction
• homogenization
• weak convergence

AMS Subject Classification (2010):

• 60G35
• 60G51
• 60H10

Acknowledgments

The author would like to thank the anonymous referee for giving useful suggestions to improve this paper.

Additional information

Funding

This work was supported by NSF of China (No. 11001051, 11371352, 12071071) and China Scholarship Council under Grant No. 201906095034.