Nonrenewal spike trains generated by stochastic neuron models

Many of the stochastic neuron models employed in the neurobiological literature generate renewal point processes, i.e., successive intervals between spikes are statistically uncorrelated. Recently, however, much experimental evidence for positive and negative correlations in the interspike interval (ISI) sequence of real neurons has been accumulated. It has been shown that these correlations can have implications for neuronal functions. We study an leaky integrate-andre (LIF) model with a dynamical threshold or an adaptation current both of which lead to negative correlations. Conditions are identi ed where these models are equivalent. The ISI statistics, the serial correlation coeÆcient, and the power spectrum of the spike train, are numerically investigated for various parameter sets.