  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.
