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math.DS2013★ 1 cited
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…
math.DS2012★ 2 cited
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…
math.DS2012
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…