Asymptotic approximations of the first three cumulants of the quasi-stationary distribution of the stochastic power law logistic model are derived. The results are based on a system of ODEs for the first three cumulants. We deviate from the classical moment closure approach by determining approximations without closing the system of equations. The approximations are explicit in the model’s parameters, conditions for validity of the approximations are given, magnitudes of approximation errors are given, and spurious solutions are easily detected and eliminated. In these ways, we provide improvements on previous results for this model.

中文翻译：

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随机幂律 Logistic 模型累积量的近似值

推导出随机幂律逻辑模型的准平稳分布的前三个累积量的渐近近似。结果基于前三个累积量的 ODE 系统。我们通过在不关闭方程组的情况下确定近似值来偏离经典的矩闭合方法。模型参数中的近似值是明确的，给出了近似值的有效性条件，给出了近似误差的大小，并且很容易检测和消除伪解。通过这些方式，我们对该模型的先前结果进行了改进。