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Effective Filtering for Multiscale Stochastic Dynamical Systems driven by Lévy processes
Huijie Qiao · 2018-10-23 · via math.PR updates on arXiv.org

The work is about multiscale stochastic dynamical systems driven by Lévy processes. First, we prove that these systems can approximate low-dimensional systems on random invariant manifolds. Second, we establish that nonlinear filterings of multiscale stochastic dynamical systems also approximate that of reduced low-dimensional systems. Finally, we investigate the reduction for $\e=0$ and obtain that these reduced systems does not approximate these multiscale stochastic dynamical systems.

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