This paper presents a new way of modeling the activity of single neurons in stochastic settings. It incorporates in a natural way many physiological mechanisms not usually found in stochastic models, such as spatial integration, non-linear membrane characteristics and non-linear interactions between excitation and inhibition. The model is based on the fact that most of the neuronal inputs have a finite lifetime. Thus, the stochastic input can be modeled as a simple finite markov chain, and the membrane potential becomes a function of the state of this chain. Firing occurs at states whose membrane potential is above threshold. The main mathematical results of the model are: (i) the input-output firing rate curve is convex at low firing rates and is saturated at high firing rates, and (ii) at low firing rates, firing usually occurs when there is synchronous convergence of many excitatory events.