{"paper":{"title":"To which extent is the membrane potential in a neuron between successive spikes adequately modelled by a (continuous) semimartingale?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["q-bio.NC"],"primary_cat":"math.PR","authors_text":"Reinhard Hoepfner","submitted_at":"2010-08-25T09:11:35Z","abstract_excerpt":"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 succe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4233","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}