Hybrid chernoff tau-leap

Alvaro Moraes, Raul Tempone, Pedro Vilanova

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Markovian pure jump processes model a wide range of phenomena, including chemical reactions at the molecular level, dynamics of wireless communication networks, and the spread of epidemic diseases in small populations. There exist algorithms such as Gillespie's stochastic simulation algorithm (SSA) and Anderson's modified next reaction method (MNRM) that simulate a single path with the exact distribution of the process, but this can be time consuming when many reactions take place during a short time interval. Gillespie's approximated tau-leap method, on the other hand, can be used to reduce computational time, but it may lead to nonphysical values due to a positive one-step exit probability, and it also introduces a time discretization error. Here, we present a novel hybrid algorithm for simulating individual paths which adaptively switches between the SSA and the tau-leap method. The switching strategy is based on a comparison of the expected interarrival time of the SSA and an adaptive time step derived from a Chernoff-type bound for the one-step exit probability. Because this bound is nonasymptotic, we do not need to make any distributional approximation for the tau-leap increments. This hybrid method allows us (i) to control the global exit probability of any simulated path and (ii) to obtain accurate and computable estimates of the expected value of any smooth observable of the process with minimal computational work. We present numerical examples that illustrate the performance of the proposed method.

Original languageEnglish (US)
Pages (from-to)581-615
Number of pages35
JournalMultiscale Modeling and Simulation
Issue number2
StatePublished - 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Chemistry
  • Modeling and Simulation
  • Ecological Modeling
  • General Physics and Astronomy
  • Computer Science Applications


  • Error control
  • Error estimates
  • Exit probability
  • Hybrid algorithms
  • Tau-leap
  • Weak approximation


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