Allen Edward J, Allen Linda J S, Schurz Henri
Department of Mathematics and Statistics, Texas Tech University, Lubbock, TX 79409-1042, USA.
Math Biosci. 2005 Jul;196(1):14-38. doi: 10.1016/j.mbs.2005.03.010.
A discrete-time Markov chain model, a continuous-time Markov chain model, and a stochastic differential equation model are compared for a population experiencing demographic and environmental variability. It is assumed that the environment produces random changes in the per capita birth and death rates, which are independent from the inherent random (demographic) variations in the number of births and deaths for any time interval. An existence and uniqueness result is proved for the stochastic differential equation system. Similarities between the models are demonstrated analytically and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models satisfy certain consistency conditions.
针对一个经历人口统计学和环境变化的种群，比较了离散时间马尔可夫链模型、连续时间马尔可夫链模型和随机微分方程模型。假设环境会导致人均出生率和死亡率产生随机变化，这些变化与任何时间间隔内出生和死亡数量的固有随机（人口统计学）变化无关。证明了随机微分方程组的一个存在唯一性结果。通过分析证明了模型之间的相似性，并给出了计算结果，以表明当模型满足某些一致性条件时，这三种随机模型的估计持续时间通常具有良好的一致性。
