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arXiv · 1008.4233

To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?

Reinhard Hoepfner
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Abstract

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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Reinhard Hoepfner. 2010-08-25. To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?. https://arxiv.org/abs/1008.4233

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