  Thought to be responsible for memory, synaptic plasticity has been widely
studied in the past few decades. One example of plasticity models is the
popular Spike Timing Dependent Plasticity (STDP). The huge litterature of STDP
models are mainly based deterministic rules whereas the biological mechanisms
involved are mainly stochastic ones. Moreover, there exist only few
mathematical studies on plasticity taking into account the precise spikes
timings. In this article, we aim at proposing a new stochastic STDP rule with
discrete synaptic weights which allows a mathematical analysis of the full
network dynamics under the hypothesis of separation of timescales. This model
attempts to answer the need for understanding the interplay between the weights
dynamics and the neurons ones.
