Lánský P, Smith C E
Math Biosci. 1989 Apr;93(2):191-215. doi: 10.1016/0025-5564(89)90023-0.
The effect of a random initial value is examined in several stochastic integrate-and-fire neural models with a constant threshold and a constant input. The three models considered are approximations of Stein's model, namely: (1) a leaky integrator with deterministic trajectories, (2) a Wiener process with drift, and (3) an Ornstein-Uhlenbeck process. For model 1, different distributions for the initial value lead to commonly observed interspike interval distributions. For model 2, a discrete and a uniform distribution for the initial value are examined along with some parameter estimation procedures. For model 3, with a truncated normal distribution for the initial value, the coefficient of variation is shown to be greater than 1, and as the threshold becomes large the first-passage-time distribution approaches an exponential distribution. The relationships among the models and between them and previous models are also discussed, along with the robustness of the model assumptions and methods of their verification. The effects of a random initial value are found to be most pronounced at high firing rates.
在几个具有恒定阈值和恒定输入的随机积分发放神经模型中，研究了随机初始值的影响。所考虑的三个模型是斯坦因模型的近似模型，即：（1）具有确定性轨迹的泄漏积分器，（2）具有漂移的维纳过程，以及（3）奥恩斯坦 - 乌伦贝克过程。对于模型1，初始值的不同分布会导致常见的峰间间隔分布。对于模型2，研究了初始值的离散分布和均匀分布以及一些参数估计程序。对于模型3，当初始值为截断正态分布时，变异系数大于1，并且随着阈值变大，首次通过时间分布趋近于指数分布。还讨论了这些模型之间以及它们与先前模型之间的关系，以及模型假设的稳健性及其验证方法。发现随机初始值的影响在高 firing 率时最为明显。
