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.