Stochastic neuron model with dynamic synapses and evolution equation of its density function

In most neural network models, neurons are viewed as the only computational units, while the synapses are treated as passive scalar parameters (weights). It has, however, long been recognized that biological synapses can exhibit rich temporal dynamics. These dynamics may have important consequences for computing and learning in biological neural systems. This paper proposes a novel stochastic model of single neuron with synaptic dynamics, which is characterized by several stochastic differential equations. From this model, we obtain the evolution equation of their density function. Furthermore, we give an approach to cut the evolution equation of the high dimensional function down to the evolution equation of one dimension function.