Adaptive Density Tracking by Quadrature for Stochastic Differential Equations

Ryleigh A. Moore; Akil Narayan

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arXiv · 2105.08148

Adaptive Density Tracking by Quadrature for Stochastic Differential Equations

Ryleigh A. Moore·Akil Narayan

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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 tensorized DTQ procedures by utilizing a flexible quadrature rule that allows for unstructured, adaptive meshes. We propose and describe the procedure for $N$-dimensions, and demonstrate that the resulting adaptive procedure is significantly more efficient than a tensorized approach. Although we consider two-dimensional examples, all our computational procedures are extendable to higher dimensional problems.

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Ryleigh A. Moore, Akil Narayan. 2021-05-17. Adaptive Density Tracking by Quadrature for Stochastic Differential Equations. https://arxiv.org/abs/2105.08148

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