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  • Kalikow decomposition for counting processes with stochastic intensity and application to simulation algorithms

  • Part of
  • Tien Cuong Phi, Eva Löcherbach, Patricia Reynaud-Bouret
  • Journal:
    Journal of Applied Probability / Volume 60 / Issue 4 / December 2023
    Published online by Cambridge University Press:
    19 May 2023, pp. 1469-1500
    Print publication:
    December 2023
    • Article
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  • We propose a new Kalikow decomposition for continuous-time multivariate counting processes, on potentially infinite networks. We prove the existence of such a decomposition in various cases. This decomposition allows us to derive simulation algorithms that hold either for stationary processes with potentially infinite network but bounded intensities, or for processes with unbounded intensities in a finite network and with empty past before zero. The Kalikow decomposition is not unique, and we discuss the choice of the decomposition in terms of algorithmic efficiency in certain cases. We apply these methods to several examples: the linear Hawkes process, the age-dependent Hawkes process, the exponential Hawkes process, and the Galves–Löcherbach process.