A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations. (31st August 2016)

• Record Type: Journal Article
• Authors: Bernal, Francisco; Acebróon, Juan A.
• Is Part Of: Communications in computational physics. Volume 20:Number 3(2016:Sep.)
• Page Start: 703
• Page End: 732
• Publication Date: 2016-08-31
• Subjects: 60G50, -- 60-08, -- 65Cxx, -- 65-02; Weak convergence, -- Feynman-Kac, -- stochastic differential equation, -- bounded diffusion, -- first-exit problem; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.OA-2015-0016
• Languages: English
• ISSNs: 1815-2406

Abstract

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 timestep h higher than . 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 ℝ 48 . The paper is self-contained and the code will be made freely downloadable.