Adaptive Density Tracking by Quadrature for Stochastic Differential Equations

Autor:	Ryleigh A. Moore, Akil Narayan
Rok vydání:	2021
Předmět:	Computational Mathematics Applied Mathematics FOS: Mathematics Mathematics - Numerical Analysis Numerical Analysis (math.NA)
DOI:	10.48550/arxiv.2105.08148
Popis:	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. Comment: 20 pages, 6 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b9c61798a1d127b9b6c2947e447ce884 Zobrazit plný text záznamu