The prelimit generator comparison approach of Stein's method
Abstract: Diffusion approximations have widespread applications in many fields, including queueing, inventory management, and Markov chain Monte Carlo algorithms, just to name a few.
The approximations usually offer better computational tractability compared to their Markov chain counterparts and at times they also offer analytical insights not available in the original model.
The recent years have seen a lot of activity around the problem of quantifying the error of diffusion approximations in steady-state using the generator comparison approach of Stein's method, which dates back to Barbour (1988). Broadly speaking, the approximation error depends on the derivatives of the solution of the Poisson equation for the diffusion process. These derivatives correspond to certain mixing properties of the diffusion process and more often than not, bounding them is too difficult. This technical issue inhibits the widespread adoption of Stein's method as a generic tool for studying approximation errors.
I will present a new spin on the traditional Stein approach. Instead of depending on PDE solution derivatives, I will show that the approximation error depends on the sensitivity of the prelimit with respect to its initial condition. At the end of the talk, the audience members will have an intuitive "test" to determine whether this methodology can bear fruit in their setting.