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.
Keywords: LIF neuronal model; Ornstein-Uhlenbeck process; colored noise; random Euler scheme; simulation.