Multidimensional counting processes and evoked neuronal activity

It is shown that the joint behaviour of n counting processes can be used for description of neuronal spike generation in a system of n neurons with various synaptic links. This multidimensional process is suggested as a model of neuronal activity evoked by either a homogeneous or an inhomogeneous stimulus during a short time period. Several situations are considered, mainly the joint activity of pairs of neurons. The probability generating functions of the process are obtained for different kinds of intensity functions. The first and second moments of the process are provided as a tool for potential comparison of the model with experimental data.