We consider a lognormal diffusion process having a multisigmoidal logistic mean, useful to model the evolution of a population which reaches the maximum level of the growth after many stages. Referring to the problem of statistical inference, two procedures to find the maximum likelihood estimates of the unknown parameters are described. One is based on the resolution of the system of the critical points of the likelihood function, and the other is on the maximization of the likelihood function with the simulated annealing algorithm. A simulation study to validate the described strategies for finding the estimates is also presented, with a real application to epidemiological data. Special attention is also devoted to the first-passage-time problem of the considered diffusion process through a fixed boundary.

翻译：我们考虑一种具有多S形逻辑均值的对数正态扩散过程，该过程可用于描述经过多个阶段达到最大增长水平的种群演化。针对统计推断问题，本文描述了两种估计未知参数最大似然值的方法：一种基于似然函数临界点方程组的求解，另一种则采用模拟退火算法对似然函数进行最大化。同时，通过模拟研究验证了所述估计策略的有效性，并将其实际应用于流行病学数据。此外，本文还重点研究了该扩散过程通过固定边界的首达时间问题。