Name:
Multilevel Hybrid Chernoff Tau-Leap.pdf
Size:
1.836Mb
Format:
PDF
Description:
Accepted Manuscript
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2015-04-08Preprint Posting Date
2014-03-12Online Publication Date
2015-04-08Print Publication Date
2016-03Permanent link to this record
http://hdl.handle.net/10754/557225
Metadata
Show full item recordAbstract
In this work, we extend the hybrid Chernoff tau-leap method to the multilevel Monte Carlo (MLMC) setting. Inspired by the work of Anderson and Higham on the tau-leap MLMC method with uniform time steps, we develop a novel algorithm that is able to couple two hybrid Chernoff tau-leap paths at different levels. Using dual-weighted residual expansion techniques, we also develop a new way to estimate the variance of the difference of two consecutive levels and the bias. This is crucial because the computational work required to stabilize the coefficient of variation of the sample estimators of both quantities is often unaffordable for the deepest levels of the MLMC hierarchy. Our method bounds the global computational error to be below a prescribed tolerance, TOL, within a given confidence level. This is achieved with nearly optimal computational work. Indeed, the computational complexity of our method is of order O(TOL−2), the same as with an exact method, but with a smaller constant. Our numerical examples show substantial gains with respect to the previous single-level approach and the Stochastic Simulation Algorithm.Citation
Multilevel hybrid Chernoff tau-leap 2015 BIT Numerical MathematicsPublisher
Springer NatureJournal
BIT Numerical MathematicsarXiv
1403.2943ae974a485f413a2113503eed53cd6c53
10.1007/s10543-015-0556-y