17 citations · 22 across the 8 of their papers we have counts for
8 papers
Identifying stochastic governing equations from data of the most probable transition trajectories
Jian Ren, Jinqiao Duan
Extracting governing stochastic differential equation models from elusive data is crucial to understand and forecast dynamics for complex systems. We devise a method to extract the…
A parameter estimation method based on random slow manifolds
Jian Ren, Jinqiao Duan
A parameter estimation method is devised for a slow-fast stochastic dynamical system, where often only the slow component is observable. By using the observations only on the slow…
Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty
Jian Ren, Jinqiao Duan, Christopher K. R. T. Jones
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtai…
Small noise approximation of center manifolds for stochastic dynamical systems
Jian Ren, Zhongkai Guo, Xianming Liu +1
This paper provides a small noise approximation for local random center manifolds of a class of stochastic dynamical systems in Euclidean space. An example is presented to illustra…
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…
Mean Exit Time and Escape Probability for a Tumor Growth System under Non-Gaussian Noise
Jian Ren, Chujin Li, Ting Gao +2
Effects of non-Gaussian stable Lévy noise on the Gompertz tumor growth model are quantified by considering the mean exit time and escape probability of the cancer cell density…