  If interspike intervals are dependent the instantaneous firing rate does not
catch important features of spike trains. In this case the conditional
instantaneous rate plays the role of the instantaneous firing rate for the case
of samples of independent interspike intervals. If the conditional distribution
of the interspikes intervals is unknown, it becomes difficult to evaluate the
conditional firing rate. We propose a non parametric estimator for the
conditional instantaneous firing rate for Markov, stationary and ergodic ISIs.
An algorithm to check the reliability of the proposed estimator is introduced
and its consistency properties are proved. The method is applied to data
obtained from a stochastic two compartment model and to in vitro experimental
data.
