年龄结构Bellman-Harris过程的Yaglom极限的Fleming-Viot选择及其在牲畜疫情监测中的应用
Fleming-Viot Selection of the Yaglom Limit for Age-Structured Bellman-Harris Processes, with Application to Livestock Epidemic Surveillance
浏览论文内容
中文总结 AI 辅助
本文构造次临界Bellman-Harris过程的Fleming-Viot粒子系统，建立强化型Yaglom定理，证明漂移条件的必要性，并将其应用于牲畜疫情监测的变化检测检验。
中文摘要 AI 辅助
本文针对一类次临界Bellman-Harris过程构造了Fleming-Viot粒子系统，证明其在粒子数量上以多项式速率选择Yaglom极限。由于寿命服从非指数分布，种群大小不具备马尔可夫性，因此分析需在年龄构型空间上进行。在此框架下，用于Galton-Watson过程的李雅普诺夫函数不再是范数型的，但仍建立了Yaglom定理，强化了经典结果：条件律以指数速率在全变差意义下收敛，衰减率由马尔萨斯参数给出。还证明了将风险率与后代法则关联的漂移条件在自然类李雅普诺夫函数中是必要的，表明其是测度值提升的特征而非估计的缺陷。最后通过牲畜疫情监测的应用示例说明该估计量，其中Yaglom极限是变化检测检验的原假设分布。
英文摘要
In this paper, we construct a Fleming-Viot particle system for a class of subcritical Bellman-Harris processes. We prove that it selects the Yaglom limit at a polynomial rate in the number of particles. Since lifetimes are non-exponential, the population size is not Markov, and the analysis must therefore be carried out on the space of age configurations. In this setting, the Lyapunov functions used for Galton-Watson processes are no longer norm-like. Nevertheless, we establish a Yaglom theorem that strengthens the classical result: the conditional laws converge in total variation at an exponential rate, with decay rate given by the Malthusian parameter. We also prove that the drift condition, which links the hazard rate to the offspring law, is necessary within a natural class of Lyapunov functions, showing that it is a feature of the measure-valued lift rather than a defect of the estimates. Finally, we illustrate the estimator through an application to livestock epidemic surveillance, where the Yaglom limit is the null distribution of a change-detection test.
