Data-driven computation methods for quasi-stationary distribution and sensitivity analysis
Abstract
This paper studies computational methods for quasi-stationary distributions (QSDs). We first proposed a data-driven solver that solves Fokker-Planck equations for QSDs. Similar as the case of Fokker-Planck equations for invariant probability measures, we set up an optimization problem that minimizes the distance from a low-accuracy reference solution, under the constraint of satisfying the linear relation given by the discretized Fokker-Planck operator. Then we use coupling method to study the sensitivity of a QSD against either the change of boundary condition or the diffusion coefficient. The 1-Wasserstein distance between a QSD and the corresponding invariant probability measure can be quantitatively estimated. Some numerical results about both computation of QSDs and their sensitivity analysis are provided.
Cite
@article{arxiv.2103.01419,
title = {Data-driven computation methods for quasi-stationary distribution and sensitivity analysis},
author = {Yao Li and Yaping Yuan},
journal= {arXiv preprint arXiv:2103.01419},
year = {2021}
}