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    Hybrid chernoff tau-leap

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    Type
    Article
    Authors
    Moraes, Alvaro cc
    Tempone, Raul cc
    Vilanova, Pedro cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Stochastic Numerics Research Group
    Date
    2014-01
    Permanent link to this record
    http://hdl.handle.net/10754/563319
    
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    Abstract
    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. © 2014 Society for Industrial and Applied Mathematics.
    Citation
    Moraes, A., Tempone, R., & Vilanova, P. (2014). Hybrid Chernoff Tau-Leap. Multiscale Modeling & Simulation, 12(2), 581–615. doi:10.1137/130925657
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    Multiscale Modeling & Simulation
    DOI
    10.1137/130925657
    ae974a485f413a2113503eed53cd6c53
    10.1137/130925657
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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