The behavior of a stochastic perfect integrate-and-fire (PIF) model of neurons is considered. The effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing Lévy-type subordinator. Using a first-passage-time formulation, we find exact expressions for the output interspike interval (ISI) statistics. Particularly, it is shown that at some parameter regimes the ISI density exhibits a multimodal structure. Moreover, it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current $\mu$, i.e., the ISI's regularity is maximized at an intermediate value of $\mu$. The features of spike statistics, analytically revealed in our study, are compared with previously obtained results for a perfect integrate-and-fire neuron model driven by dichotomous noise (without subordination).

中文翻译：

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瞬态从属词对二分噪声驱动的神经元模型的放电统计的影响。

考虑了神经元的随机完美整合和发射（PIF）模型的行为。突触输入的时间相关的随机活动的影响被建模为不对称二分音噪声和随机操作时间的组合，其形式为反严格增加的Lévy型从属。使用首次通过时间公式，我们找到了输出尖峰间间隔（ISI）统计信息的精确表达式。特别地，显示出在某些参数范围，ISI密度表现出多峰结构。此外，证明了变异系数，序列相关系数和Fano因子对平均输入电流表现出非单调依赖性。$\mu$，即ISI的规律性在中间值为时最大化 $\mu$。在我们的研究中分析揭示的峰值统计数据的特征与先前获得的结果进行了比较，结果是由二分噪声（无从属关系）驱动的理想的积分并发射神经元模型。