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5 papers · 2 filters
Topological equivalence for discontinuous random dynamical systems and applications
Huijie Qiao, Jinqiao Duan
After defining non-Gaussian Lévy processes for two-sided time, stochastic differential equations with such Lévy processes are considered. Solution paths for these stochastic differ…
Stationary Measures for Stochastic Differential Equations with Jumps
Huijie Qiao, Jinqiao Duan
In the paper, stationary measures of stochastic differential equations with jumps are considered. Under some general conditions, existence of stationary measures is proved through…
Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems
Hongbo Fu, Xianming Liu, Jinqiao Duan
This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of f…
A Multiplicative Ergodic Theorem for Discontinuous Random Dynamical Systems and Applications
Huijie Qiao, Jinqiao Duan
Motivated by studying stochastic systems with non-Gaussian Lévy noise, spectral properties for a type of linear cocycles are considered. These linear cocycles have countable jump d…
Asymptotic methods for stochastic dynamical systems with small non-Gaussian Lévy noise
Huijie Qiao, Jinqiao Duan
The goal of the paper is to analytically examine escape probabilities for dynamical systems driven by symmetric -stable Lévy motions. Since escape probabilities are solutions of…