Effective Filtering for Multiscale Stochastic Dynamical Systems driven by L\'evy processes

Huijie Qiao

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arXiv · 1810.10370

Effective Filtering for Multiscale Stochastic Dynamical Systems driven by L\'evy processes

Huijie Qiao

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Abstract

The work is about multiscale stochastic dynamical systems driven by L\'evy 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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Huijie Qiao. 2018-10-23. Effective Filtering for Multiscale Stochastic Dynamical Systems driven by L\'evy processes. https://arxiv.org/abs/1810.10370

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