
Yao Li 
University of Massachusetts, Amherst, Department of Mathematics and Statistics 
3:00 pm in MSB 318


Consider a stochastic process (such as a stochastic differential equation) arising from applications. In practice, we are interested in many things like the (invariant) probability density function of this process, the speed of convergence to the invariant probability measure, and the difference between two invariant measures given by the exact random process and its numerical approximation. Rigorous estimates for these problems are available, but usually far from being sharp. In this talk I will introduce a few datadriven computational methods that solve these problems for a class of stochastic dynamical systems, including but not limited to stochastic differential equations. All these methods are driven by simulation data. Hence they are much less affected by the curseofdimensionality than traditional gridbased methods. I will demonstrate a few high (up to 100) dimensional examples in my talk. 