Convergence of nonlinear filterings for stochastic dynamical systems with Lévy noises. (English) Zbl 1492.60100
Summary: 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.
MSC:
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 60G51 | Processes with independent increments; Lévy processes |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
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