Adaptive Density Tracking by Quadrature for Stochastic Differential Equations

2021/05/17 by Ryleigh A. Moore, Moore, Ryleigh A., Akil Narayan +1 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2105.08148

openalex publication_date 2021/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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