论文标题
雅各比作为神经元模型的跳跃过程：第一个通道时间分析
Jacobi processes with jumps as neuronal models: a first passage time analysis
论文作者
论文摘要
为了克服经典神经元模型的某些限制，我们通过引入向下跳跃来描述单个神经元的活性，提出了基于雅各比过程的经典模型的马尔可夫概括。尖峰间隔的统计分析是通过研究拟议的马尔可夫雅各比过程的首次计时时间进行的，并通过恒定边界跳跃。特别是，我们表征了其拉普拉斯变换，该变换是根据我们引入的高几幅函数的某些概括来表达的，并推断出其期望的封闭式表达。我们的方法是在第一次通过时间问题的背景下是原始的，它依赖于经典雅各比过程的半群之间的关系及其概括，这是最近在[11]中建立的。对所涉及的参数和跳跃分布的某些选择，对考虑的神经元的发射率进行了数值研究。
To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of inter-spike intervals is performed by studying the first-passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform which is expressed in terms of some generalization of hypergeometric functions that we introduce, and deduce a closed-form expression for its expectation. Our approach, which is original in the context of first passage time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization, which have been recently established in [11]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jumps distributions.
