title: How sample paths of leaky integrate-and-fire models are influenced by the presence of a firing threshold.
abstract: Neural membrane potential data are necessarily conditional on observation being prior to a firing time. In a stochastic leaky integrate-and-fire model, this corresponds to conditioning the process on not crossing a boundary. In the literature, simulation and estimation have almost always been done using unconditioned processes. In this letter, we determine the stochastic differential equations of a diffusion process conditioned to stay below a level S up to a fixed time t(1) and of a diffusion process conditioned to cross the boundary for the first time at t(1). This allows simulation of sample paths and identification of the corresponding mean process. Differences between the mean of free and conditioned processes are illustrated, as well as the role of noise in increasing these differences.
authors.affiliation: Department of Mathematics G. Peano, University of Turin, 10123 Turin, Italy. mariateresa.giraudo@unito.it
authors.forename: Maria Teresa
authors.initials: MT
authors.lastname: Giraudo
authors.forename: Priscilla E
authors.initials: PE
authors.lastname: Greenwood
authors.forename: Laura
authors.initials: L
authors.lastname: Sacerdote
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D008564:Membrane Potentials / Q000502:physiology; D008959:Models, Neurological; D012684:Sensory Thresholds / Q000502:physiology; D013269:Stochastic Processes