A coupling approach in the computation of geometric ergodicity for stochastic dynamics

This talk introduces a probabilistic approach to numerically compute geometric convergence rates in discrete or continuous stochastic systems. Choosing appropriate coupling mechanisms and combining them together, works well in many settings, especially in high-dimensions. Using this approach, it is observed that the rate of geometric ergodicity of a randomly perturbed system can, to some extent, reveal the degree of chaoticity of the unperturbed system. Potential applications of the coupling method and the visualization of higher dimensional non-convex functions, e.g., the loss functions of neural networks, will be discussed.