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This paper studies computational methods for quasi-stationary distributions(QSDs). We first proposed a data-driven solver that solves Fokker-Planckequations for QSDs. Similar as the case of Fokker-Planck equations forinvariant probability measures, we set up an optimization problem thatminimizes the distance from a low-accuracy reference solution, under theconstraint of satisfying the linear relation given by the discretizedFokker-Planck operator. Then we use coupling method to study the sensitivity ofa QSD against either the change of boundary condition or the diffusioncoefficient. The 1-Wasserstein distance between a QSD and the correspondinginvariant probability measure can be quantitatively estimated. Some numericalresults about both computation of QSDs and their sensitivity analysis areprovided.

Data-driven computation methods for quasi-stationary distribution and sensitivity analysis