To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?
Probability
2010-08-26 v1 Neurons and Cognition
Abstract
We consider -variations in some membrane potential data --viewed as a function of the step size in case where is fixed, or viewed as a function of 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.
Cite
@article{arxiv.1008.4233,
title = {To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?},
author = {Reinhard Hoepfner},
journal= {arXiv preprint arXiv:1008.4233},
year = {2010}
}