  We consider a class of spiking neuronal models, defined by a set of
conditions typical for basic threshold-type models, such as the leaky
integrate-and-fire or the binding neuron model and also for some artificial
neurons. A neuron is fed with a Poisson process. Each output impulse is applied
to the neuron itself after a finite delay $\Delta$. This impulse acts as being
delivered through a fast Cl-type inhibitory synapse. We derive a general
relation which allows calculating exactly the probability density function
(pdf) $p(t)$ of output interspike intervals of a neuron with feedback based on
known pdf $p^0(t)$ for the same neuron without feedback and on the properties
of the feedback line (the $\Delta$ value). Similar relations between
corresponding moments are derived. Furthermore, we prove that initial segment
of pdf $p^0(t)$ for a neuron with a fixed threshold level is the same for any
neuron satisfying the imposed conditions and is completely determined by the
input stream. For the Poisson input stream, we calculate that initial segment
exactly and, based on it, obtain exactly the initial segment of pdf $p(t)$ for
a neuron with feedback. That is the initial segment of $p(t)$ is
model-independent as well. The obtained expressions are checked by means of
Monte Carlo simulation. The course of $p(t)$ has a pronounced peculiarity,
which makes it impossible to approximate $p(t)$ by Poisson or another simple
stochastic process.
