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Limit theorems for cloning algorithms

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  • Angeli, Letizia
  • Grosskinsky, Stefan
  • Johansen, Adam M.

Abstract

Large deviations for additive path functionals of stochastic processes have attracted significant research interest, in particular in the context of stochastic particle systems and statistical physics. Efficient numerical ‘cloning’ algorithms have been developed to estimate the scaled cumulant generating function, based on importance sampling via cloning of rare event trajectories. So far, attempts to study the convergence properties of these algorithms in continuous time have led to only partial results for particular cases. Adapting previous results from the literature of particle filters and sequential Monte Carlo methods, we establish a first comprehensive and fully rigorous approach to bound systematic and random errors of cloning algorithms in continuous time. To this end we develop a method to compare different algorithms for particular classes of observables, based on the martingale characterization of stochastic processes. Our results apply to a large class of jump processes on compact state space, and do not involve any time discretization in contrast to previous approaches. This provides a robust and rigorous framework that can also be used to evaluate and improve the efficiency of algorithms.

Suggested Citation

  • Angeli, Letizia & Grosskinsky, Stefan & Johansen, Adam M., 2021. "Limit theorems for cloning algorithms," Stochastic Processes and their Applications, Elsevier, vol. 138(C), pages 117-152.
    • Handle: RePEc:eee:spapps:v:138:y:2021:i:c:p:117-152
    DOI: 10.1016/j.spa.2021.04.007
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    References listed on IDEAS

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    1. Moral, P. Del & Miclo, L., 2000. "A Moran particle system approximation of Feynman-Kac formulae," Stochastic Processes and their Applications, Elsevier, vol. 86(2), pages 193-216, April.
    2. Nick Whiteley & Nikolas Kantas, 2017. "Calculating Principal Eigen-Functions of Non-Negative Integral Kernels: Particle Approximations and Applications," Mathematics of Operations Research, INFORMS, vol. 42(4), pages 1007-1034, November.
    3. Ryszard Kutner & Jaume Masoliver, 2017. "The continuous time random walk, still trendy: fifty-year history, state of art and outlook," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(3), pages 1-13, March.
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    Cited by:

    1. Cloez, Bertrand & Corujo, Josué, 2022. "Uniform in time propagation of chaos for a Moran model," Stochastic Processes and their Applications, Elsevier, vol. 154(C), pages 251-285.

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