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Data-Driven Computational Methods for Quasi-Stationary Distribution and Sensitivity Analysis

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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 to 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.

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  1. Department of Mathematics and Statistics, University of Massachusetts Amherst, Amherst, MA, 01002, USA

    Yao Li & Yaping Yuan

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  1. Yao Li
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  2. Yaping Yuan
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Correspondence to Yao Li.

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Yao Li is partially supported by NSF DMS-1813246 and DMS-2108628.

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Li, Y., Yuan, Y. Data-Driven Computational Methods for Quasi-Stationary Distribution and Sensitivity Analysis. J Dyn Diff Equat 35, 2069–2097 (2023). https://doi.org/10.1007/s10884-022-10137-2

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  • DOI: https://doi.org/10.1007/s10884-022-10137-2

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