title: The Gamma renewal process as an output of the diffusion leaky integrate-and-fire neuronal model.
abstract: Statistical properties of spike trains as well as other neurophysiological data suggest a number of mathematical models of neurons. These models range from entirely descriptive ones to those deduced from the properties of the real neurons. One of them, the diffusion leaky integrate-and-fire neuronal model, which is based on the Ornstein-Uhlenbeck (OU) stochastic process that is restricted by an absorbing barrier, can describe a wide range of neuronal activity in terms of its parameters. These parameters are readily associated with known physiological mechanisms. The other model is descriptive, Gamma renewal process, and its parameters only reflect the observed experimental data or assumed theoretical properties. Both of these commonly used models are related here. We show under which conditions the Gamma model is an output from the diffusion OU model. In some cases, we can see that the Gamma distribution is unrealistic to be achieved for the employed parameters of the OU process.
authors.affiliation: Institute of Physiology, Academy of Sciences of Czech Republic, Videnská 1083, 142 20, Prague 4, Czech Republic.
authors.forename: Petr
authors.initials: P
authors.lastname: Lansky
authors.affiliation: Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123, Torino, Italy.
authors.forename: Laura
authors.initials: L
authors.lastname: Sacerdote
authors.affiliation: Department of Mathematics "G. Peano", University of Torino, Via Carlo Alberto 10, 10123, Torino, Italy. cristina.zucca@unito.it.
authors.forename: Cristina
authors.initials: C
authors.lastname: Zucca
mesh_terms: D003491:Cybernetics; D004058:Diffusion; D008959:Models, Neurological; D009474:Neurons; D013269:Stochastic Processes
keywords: First-passage-time problem; Leaky integrate-and-fire; Stein’s neuronal model