Adaptive density tracking by quadrature for stochastic differential equations

Ryleigh A. Moore and Akil Narayan

Applied Mathematics and Computation, 2022, vol. 431, issue C

Abstract: Density tracking by quadrature (DTQ) is a numerical procedure for computing solutions to Fokker-Planck equations that describe probability densities for stochastic differential equations (SDEs). In this paper, we extend upon existing trapezoidal quadrature rule DTQ procedures by utilizing a flexible quadrature rule that allows for unstructured, adaptive meshes. We describe the procedure for N-dimensions, and demonstrate that the resulting adaptive procedure can be significantly more efficient than the trapezoidal DTQ method. We show examples of our procedure for problems ranging from one to five dimensions.

Keywords: Stochastic differential equations; Leja points; Numerical methods (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:431:y:2022:i:c:s0096300322003721

DOI: 10.1016/j.amc.2022.127298

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