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Birth Death Swap population in random environment and aggregation with two timescales

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  • Kaakai, Sarah
  • El Karoui, Nicole

Abstract

This paper deals with the stochastic modeling of a class of heterogeneous population in random environment, structured by discrete subgroups, and called birth–death–swap. In addition to demographic events modifying the population size, swap events, i.e. moves between subgroups, occur in the population. Event intensities are random functionals of the population. In the first part, we show that the complexity of the problem is significantly reduced by modeling the jump measure of the population as a multivariate counting process. This process is defined as the solution of a stochastic differential system with random coefficients, driven by a multivariate Poisson random measure. The solution is obtained under weak assumptions, by the thinning of a strongly dominating point process generated by the same Poisson measure. This key construction relies on a general strong comparison result, of independent interest.

Suggested Citation

  • Kaakai, Sarah & El Karoui, Nicole, 2023. "Birth Death Swap population in random environment and aggregation with two timescales," Stochastic Processes and their Applications, Elsevier, vol. 162(C), pages 218-248.
    • Handle: RePEc:eee:spapps:v:162:y:2023:i:c:p:218-248
    DOI: 10.1016/j.spa.2023.04.017
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    References listed on IDEAS

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    1. Song, Li-Peng & Jin, Zhen & Sun, Gui-Quan, 2011. "Modeling and analyzing of botnet interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 347-358.
    2. Booth, H. & Tickle, L., 2008. "Mortality Modelling and Forecasting: a Review of Methods," Annals of Actuarial Science, Cambridge University Press, vol. 3(1-2), pages 3-43, September.
    3. Nicole El Karoui & Kaouther Hadji & Sarah Kaakai, 2021. "Simulating long-term impacts of mortality shocks: learning from the cholera pandemic," Papers 2111.08338, arXiv.org.
    4. Rolski, T. & Szekli, R., 1991. "Stochastic ordering and thinning of point processes," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 299-312, April.
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