| 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 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 simulation data. Hence they are much 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. |