Open AccessOn a stochastic neuronal model integrating correlated inputs
Author(s) -
Giacomo Ascione,
Enrica Pirozzi
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - Uncategorized
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019260
Subject(s) - covariance , equivalence (formal languages) , white noise , stochastic modelling , stochastic process , ornstein–uhlenbeck process , noise (video) , mathematics , reset (finance) , stochastic simulation , computer science , statistical physics , statistics , physics , artificial intelligence , discrete mathematics , financial economics , economics , image (mathematics)
A modified LIF-type stochastic model is considered with a non-delta correlated stochastic process in place of the traditional white noise. Two different mechanisms of reset are specified with the aim to model endogenous and exogenous correlated input stimuli. Ornstein-Uhlenbeck processes are used to model the two different cases. An equivalence between different ways to include currents in the model is also shown. The theory of integrated stochastic processes is evoked and the main features of involved processes are obtained, such as mean and covariance functions. Finally, a simulation algorithm of the proposed model is described; simulations are performed to provide estimations of firing densities and related comparisons are given.