Diffusion approximations for Lotka-Volterra type models
Diffusion approximations for Lotka-Volterra type models
复制标题
Lotka-Volterra 类型模型的扩散近似
DOI：
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
M. J. Rosales
中科院分区：
文献类型：
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作者：
R. Gutiérrez;M. J. Rosales
我们得到了两个二元人口增长模型的扩散近似。每当相应的马尔可夫人口过程在分析上难以处理时，这些都很有用。在出生和死亡过程的背景下，我们考虑随机版本的确定性模型的Lotka -沃尔泰拉型，一个模型的物种竞争和捕食模型，都与对数的相互作用。我们得到了一个扩散近似，它表明，随着资源的大小趋于无穷大，适当的缩放和规范化的过程收敛到非平稳的Ornstein-Uhlenbeck过程。此外，我们已经确定了从什么顺序的过程是很好地近似的极限扩散。最后，在均匀的情况下，我们已经确定了从什么顺序向前的物种大小成为，在稳定状态下，平稳高斯过程。我们推导出每个模型的均值向量和协方差
We obtain diffusion approximations for two bivariate models of population growth. These are useful whenever the corresponding Markov population processes are analytically intractable. In the context of birth and death processes, we consider stochastic versions of the deterministic models of Lotka – Volterra type, a model of species competition and a prey-predator model, both with logarithmic interactions. We obtain a diffusion approximation which show that, as the resource-sizes tend to infinity, the suitably scaled and normalized processes converge to non-stationary Ornstein – Uhlenbeck processes. Furthermore, we have determined from what order on the processes are well approximated by the limiting diffusions. Finally, in the homogenous situation, we have determined from what order onward the species sizes become, in the steady state, stationary Gaussian processes. We derive the mean vector and covariance for each model