Multilevel hybrid Chernoff tau-leap

Alvaro Moraes, Raúl Tempone, Pedro Vilanova

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)189-239
Number of pages51
JournalBIT Numerical Mathematics
Issue number1
StatePublished - Mar 1 2016
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics


  • Chernoff tau-leap
  • Computational Complexity
  • Continuous time Markov chains
  • Dual-weighted estimation
  • Global error control
  • Hybrid simulation methods
  • Multilevel Monte Carlo
  • Stochastic reaction networks
  • Strong error estimation


Dive into the research topics of 'Multilevel hybrid Chernoff tau-leap'. Together they form a unique fingerprint.

Cite this