TY - JOUR
T1 - Multilevel hybrid Chernoff tau-leap
AU - Moraes, Alvaro
AU - Tempone, Raúl
AU - Vilanova, Pedro
N1 - Publisher Copyright:
© 2015, Springer Science+Business Media Dordrecht.
PY - 2016/3/1
Y1 - 2016/3/1
N2 - 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 (Formula presented.) , 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.
AB - 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 (Formula presented.) , 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.
KW - Chernoff tau-leap
KW - Computational Complexity
KW - Continuous time Markov chains
KW - Dual-weighted estimation
KW - Global error control
KW - Hybrid simulation methods
KW - Multilevel Monte Carlo
KW - Stochastic reaction networks
KW - Strong error estimation
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U2 - 10.1007/s10543-015-0556-y
DO - 10.1007/s10543-015-0556-y
M3 - Article
AN - SCOPUS:84927544578
SN - 0006-3835
VL - 56
SP - 189
EP - 239
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 1
ER -