在何种程度上，连续尖峰之间的神经元的膜电位可以被（连续）半鞅充分模拟？
To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?
摘要：
我们考虑$p$ --某些膜电位数据的变化--在$p$固定的情况下被视为步长的函数，或在步长固定的情况下被视为$p$的函数--并将其形状与Ait-Sahalia和Jacod（2009）中的结果进行比较，后者确实适用于一般的半鞅。我们得到以下结论：在非或很少尖峰的情况下，膜电位表现为半鞅，在某些情况下，作为一个跳跃的半鞅。一旦神经元发放脉冲，半鞅模型不再适用于连续脉冲之间的膜电位，即使脉冲间间隔相对较长。
英文摘要：
We consider $p$-variations in some membrane potential data --viewed as a function of the step size in case where $p$ is fixed, or viewed as a function of $p$ in case where the step size is fixed-- and compare their shape with results in Ait-Sahalia and Jacod (2009) which do hold for general semimartingales. We obtain the following conclusion: in non- or very rarely spiking cases the membrane potential behaves as a semimartingale, in some cases as a semimartingale with jumps. Once the neuron is spiking, a semimartingale modelization is no longer adequate for the membrane potential between successive spikes, even if interspike intervals are relatively long.
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