Ergodicity of stochastically forced large scale geophysical flows.
Heteroclinic points of multi-dimensional dynamical systems.
Escape probability and mean residence time in random flows with unsteady drift.
Synchronization of dissipative dynamical systems driven by non-Gaussian Lev́y noises.
State estimation under non-Gaussian Lévy noise: A modified Kalman filtering method
The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems with non-Gaussian Lévy noise is devised. It works effectively with reasonable computational cost. Simulation results are presented to illustrate this non-Gaussian filtering method.
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