We present exact analytical expressions of moments of all orders for neuronal membrane potentials in the multiplicative nonstationary Poisson shot noise model. As an application, we derive closed-form Gram–Charlier density expansions that show how the probability density functions of potentials in such models differ from their Gaussian diffusion approximations. This approach extends the results of Brigham and Destexhe (Preprint, 2015a; Phys Rev E 91:062102, 2015b) by the use of exact combinatorial expressions for the moments of multiplicative nonstationary filtered shot noise processes. Our results are confirmed by stochastic simulations and apply to single- and multiple-noise-source models.

我们提出了乘法非平稳泊松散粒噪声模型中神经元膜电位所有阶矩的精确解析表达式。作为一个应用，我们推导出封闭形式的 Gram-Charlier 密度展开式，以显示此类模型中势的概率密度函数与其高斯扩散近似值有何不同。这种方法通过使用乘法非平稳滤波散粒噪声过程的矩的精确组合表达式扩展了 Brigham 和 Destexhe（预印本，2015a；Phys Rev E 91：062102，2015b）的结果。我们的结果通过随机模拟得到证实，并适用于单噪声源和多噪声源模型。