Volume 20, Issue 3
A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

Francisco Bernal & Juan A. Acebrón

Commun. Comput. Phys., 20 (2016), pp. 703-732.

Published online: 2018-04

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  • Abstract

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the time step $h$ higher than $\mathcal{O}$$(√h)$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to R48. The paper is self-contained and the code will be made freely downloadable.

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@Article{CiCP-20-703, author = {Francisco Bernal , and Juan A. Acebrón , }, title = {A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {20}, number = {3}, pages = {703--732}, abstract = {

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the time step $h$ higher than $\mathcal{O}$$(√h)$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to R48. The paper is self-contained and the code will be made freely downloadable.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2015-0016}, url = {http://global-sci.org/intro/article_detail/cicp/11170.html} }
TY - JOUR T1 - A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations AU - Francisco Bernal , AU - Juan A. Acebrón , JO - Communications in Computational Physics VL - 3 SP - 703 EP - 732 PY - 2018 DA - 2018/04 SN - 20 DO - http://doi.org/10.4208/cicp.OA-2015-0016 UR - https://global-sci.org/intro/article_detail/cicp/11170.html KW - AB -

We review, implement, and compare numerical integration schemes for spatially bounded diffusions stopped at the boundary which possess a convergence rate of the discretization error with respect to the time step $h$ higher than $\mathcal{O}$$(√h)$. We address specific implementation issues of the most general-purpose of such schemes. They have been coded into a single Matlab program and compared, according to their accuracy and computational cost, on a wide range of problems in up to R48. The paper is self-contained and the code will be made freely downloadable.

Francisco Bernal & Juan A. Acebrón. (2020). A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations. Communications in Computational Physics. 20 (3). 703-732. doi:10.4208/cicp.OA-2015-0016
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