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We consider $p$-variations in some membrane potential data --viewed as afunction of the step size in case where $p$ is fixed, or viewed as a functionof $p$ in case where the step size is fixed-- and compare their shape withresults in Ait-Sahalia and Jacod (2009) which do hold for generalsemimartingales. We obtain the following conclusion: in non- or very rarelyspiking cases the membrane potential behaves as a semimartingale, in some casesas a semimartingale with jumps. Once the neuron is spiking, a semimartingalemodelization is no longer adequate for the membrane potential betweensuccessive spikes, even if interspike intervals are relatively long.

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