Georgia Institute of Technology College of Sciences

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 measure, the sensitivity of the invariant probability measure, and the speed of convergence to the invariant probability measure. Existing rigorous estimates of these problems usually cannot provide enough details. In this talk I will introduce a few data-driven 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 the simulation data, and are less affected by the curse-of-dimensionality than traditional grid-based methods. I will demonstrate a few high (up to 100) dimensional examples in my talk.