  Spike generation in neurons produces a temporal point process, whose
statistics is governed by intrinsic phenomena and the external incoming inputs
to be coded. In particular, spike-evoked adaptation currents support a slow
temporal process that conditions spiking probability at the present time
according to past activity. In this work, we study the statistics of interspike
interval correlations arising in such non-renewal spike trains, for a neuron
model that reproduces different spike modes in a small adaptation scenario. We
found that correlations are stronger as the neuron fires at a particular firing
rate, which is defined by the adaptation process. When set in a subthreshold
regime, the neuron may sustain this particular firing rate, and thus induce
correlations, by noise. Given that, in this regime, interspike intervals are
negatively correlated at any lag, this effect surprisingly implies a reduction
in the variability of the spike count statistics at a finite noise intensity.
