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We present a mathematical model of a biological synapse based on stochastic processes to establish the temporal behavior of the postsynaptic potential following a quantal synaptic transmission. This potential form is the basis of the neural code. We suppose that the release of neurotransmitters in the synaptic cleft follows a Poisson process, and that they diffuse according to integrated Ornstein-Uhlenbeck processes in 3-D with random initial positions and velocities. The diffusion occurs in an isotropic environment between two infinite parallel planes representing the pre- and postsynaptic membrane. We state that the presynaptic membrane is perfectly reflecting and that the other is perfectly absorbing. The activation of the receptors polarizes the postsynaptic membrane according to a parallel RC circuit scheme. We present the results obtained by simulations according to a Gillespie algorithm and we show that our model exhibits realistic postsynaptic behaviors from a simple quantal occurrence.