  Negative serial correlations in single spike trains are an effective method
to reduce the variability of spike counts. One of the factors contributing to
the development of negative correlations between successive interspike
intervals is the presence of adaptation currents. In this work, based on a
hidden Markov model and a proper statistical description of conditional
responses, we obtain analytically these correlations in an adequate dynamical
neuron model resembling adaptation. We derive the serial correlation
coefficients for arbitrary lags, under a small adaptation scenario. In this
case, the behavior of correlations is universal and depends on the first-order
statistical description of an exponentially driven time-inhomogeneous
stochastic process.
