A Comparison of Higher-Order Weak Numerical Schemes for Stopped Stochastic Differential Equations

被引：10

作者：

Bernal, Francisco ^{[1
,2
]}

Acebron, Juan A. ^{[1
,3
]}

机构：

[1] Univ Tecn Lisboa, INESC ID IST, Rua Alves Redol 9, P-1000029 Lisbon, Portugal

[2] Inst Super Tecn, Dept Math, Ctr Math & Its Applicat, Av Rovisco Pais, P-1049001 Lisbon, Portugal

[3] ISCTE Inst Univ Lisboa, Dept Ciencias & Tecnol Informacao, Av Forcas Armadas, P-1649026 Lisbon, Portugal

来源：

COMMUNICATIONS IN COMPUTATIONAL PHYSICS | 2016年 / 20卷 / 03期

关键词：

Weak convergence; Feynman-Kac; stochastic differential equation; bounded diffusion; first-exit problem; MONTE-CARLO METHODS; EXIT TIMES; APPROXIMATION; PROBABILITY; SIMULATION; ALGORITHM; DOMAIN;

D O I：

10.4208/cicp.OA-2015-0016

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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 O(root 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 R-48. The paper is self-contained and the code will be made freely downloadable.

引用

页码：703 / 732

页数：30

共 36 条

[1] Domain decomposition solution of elliptic boundary-value problems via Monte Carlo and quasi-Monte Carlo methods [J].