  In spiking neural networks, the information is conveyed by the spike times,
that depend on the intrinsic dynamics of each neuron, the input they receive
and on the connections between neurons. In this article we study the Markovian
nature of the sequence of spike times in stochastic neural networks, and in
particular the ability to deduce from a spike train the next spike time, and
therefore produce a description of the network activity only based on the spike
times regardless of the membrane potential process.
  To study this question in a rigorous manner, we introduce and study an
event-based description of networks of noisy integrate-and-fire neurons, i.e.
that is based on the computation of the spike times. We show that the firing
times of the neurons in the networks constitute a Markov chain, whose
transition probability is related to the probability distribution of the
interspike interval of the neurons in the network. In the cases where the
Markovian model can be developed, the transition probability is explicitly
derived in such classical cases of neural networks as the linear
integrate-and-fire neuron models with excitatory and inhibitory interactions,
for different types of synapses, possibly featuring noisy synaptic integration,
transmission delays and absolute and relative refractory period. This covers
most of the cases that have been investigated in the event-based description of
spiking deterministic neural networks.
