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First Passage Time Problem for the Ornstein-Uhlenbeck Neuronal Model

机译:Ornstein-Uhlenbeck神经元模型的首次通过时间问题

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摘要

In this paper we propose a simple and efficient method for computing accurate estimates (in closed form) of the first passage time density of the Ornstein-Uhlenbeck neuronal model through a fixed boundary (i.e. the interspike statistics of the stochastic leaky integrate-and-fire neuron model). This new approach can also provide very tight upper and lower bounds (in closed form) for the exact first passage time density in a systematic manner. Unlike previous approximate analytical attempts, this novel approximation scheme not only goes beyond the linear response and weak noise limit, but it can also be systematically improved to yield the exact results. Furthermore, it is straightforward to extend our approach to study the more general case of a deterministically modulated boundary.
机译:在本文中,我们提出了一种简单有效的方法,用于通过固定边界来计算Ornstein-Uhlenbeck神经元模型的第一次通过时间密度的精确估计(以封闭形式)(即,随机泄漏的积分和发射的尖峰统计)神经元模型)。这种新方法还可以以系统的方式为精确的第一次通过时间密度提供非常紧密的上下边界(以封闭形式)。与以前的近似分析尝试不同,这种新颖的近似方案不仅超越了线性响应和弱噪声限制,而且还可以系统地加以改进以产生准确的结果。此外,很容易将我们的方法扩展为研究确定性调制边界的更一般情况。

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