Neuronal behavior is dependent on random inputs from a multitude of synaptic contacts on the soma and dendritic tree. Therefore, simulations of different types of noise are often required in the experimental and theoretical investigation of the properties of neurons and neuronal assemblies. The direct simulation of these noise sources by simple difference equations may therefore be quite useful and a general approach is presented in this paper. Initially, a first order model and its time-discretization are analyzed in detail, followed by a generalization to more complex models. The firing patterns of neurons are dependent on the random behaviors of their membrane potentials at the trigger zone. These depend on the propagation of the randomly occurring postsynaptic potentials from specific places on the dendritic tree or soma to the trigger zone. Different models may represent a variety of circumstances in which random membrane potentials arise at the trigger zone. Simulations of different types of noise are often required in the experimental and theoretical investigation of the properties of neurons and neuronal assemblies. The direct simulation of these noise sources by simple difference equations may therefore be quite useful and a general approach is presented in this paper. This paper presents a detailed analysis of the very useful first order model and its time discretization. The criterion used is that the autocovariance sequence of the discrete time model be a sample of the original autocovariance function. Several cases are presented which are of practical interest, including the case of constant output variance independent of the model's time constant. General models are time-discretized by the impulse response invariance method. Two applications are presented, one is related to the modeling of the synaptic currents by the alpha function instead of the delta function and the second deals with analog synaptic noise generation by D/A conversion of computer generated noise sequences.