182 citations · 1.5k across the 227 of their papers we have counts for
7 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…
Ensemble Averaging for Dynamical Systems under Fast Oscillating Random Boundary Conditions
Wei Wang, Jian Ren, Jinqiao Duan +1
This paper is devoted to provide a theoretical underpinning for ensemble forecasting with rapid fluctuations in body forcing and in boundary conditions. Ensemble averaging principl…
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…
Quantifying Model Uncertainties in the Space of Probability Measures
Jinqiao Duan, Ting Gao, Guowei He
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus con…
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…