Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo
Type
Conference PaperKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2016-06-14Online Publication Date
2016-06-14Print Publication Date
2016Permanent link to this record
http://hdl.handle.net/10754/622138
Metadata
Show full item recordAbstract
A formal mean square error expansion (MSE) is derived for Euler-Maruyama numerical solutions of stochastic differential equations (SDE). The error expansion is used to construct a pathwise, a posteriori, adaptive time-stepping Euler-Maruyama algorithm for numerical solutions of SDE, and the resulting algorithm is incorporated into a multilevel Monte Carlo (MLMC) algorithm for weak approximations of SDE. This gives an efficient MSE adaptive MLMC algorithm for handling a number of low-regularity approximation problems. In low-regularity numerical example problems, the developed adaptive MLMC algorithm is shown to outperform the uniform time-stepping MLMC algorithm by orders of magnitude, producing output whose error with high probability is bounded by TOL > 0 at the near-optimal MLMC cost rate б(TOL log(TOL)) that is achieved when the cost of sample generation is б(1).Citation
Hoel H, Häppölä J, Tempone R (2016) Construction of a Mean Square Error Adaptive Euler–Maruyama Method With Applications in Multilevel Monte Carlo. Monte Carlo and Quasi-Monte Carlo Methods: 29–86. Available: http://dx.doi.org/10.1007/978-3-319-33507-0_2.Publisher
Springer NatureConference/Event name
11th International Conference on Monte Carlo and Quasi Monte Carlo Methods in Scientific Computing, MCQMC 2014arXiv
1411.5515ae974a485f413a2113503eed53cd6c53
10.1007/978-3-319-33507-0_2