Deep brain stimulation (DBS) is a highly promising therapy for Parkinson's disease (PD). However, most patients do not get full therapeutic benefit from DBS yet, due to its critical dependence on electrode location. For this reason, we believe that the investigation of a neural modeling, estimation and control framework for the STN is an interesting research problem. This would pave the way for the development of a novel surgical tool for the DBS placement standardization, i.e., an automated intraoperative closed-loop DBS localization system. A fundamental problem to be solved for the realization of a such framework is the neurophysiologic characterization of the STN activity. Indeed, this would allow to understand if the modeling of the sweet spot is feasible. In this paper an effort towards the modeling of the neuronal activity near the stimulation target is made: first we analyze single unit spiking activity of 120 STN neurons collected from four PD patients at different distances from the sweet spot and, for each neuron, we estimate a point process model (PPM). Then, we see that PPMs capture the stochastic effects of the distance from the sweet spot on the STN spiking activity, and characterize the impact of local neuronal networks on the single neurons. Our results suggest that PPMs might be an effective tool for modeling of the STN neuronal activities accounting for the depth within it.