The paper presents two new families of stochastic processes called hyperkernel convolution train and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -counting processes. These models generalize respectively the spike train and counting process models. The convolution train model is designed to encompass both continuous and singular spiking activities. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -counting process can be used to model counting phenomena for which the increments are not necessarily instantaneous. This <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</i> -counting model can also be used to represent uncertainties on the exact locations of state transitions of a standard discrete event system. The paper also highlights some statistical properties of the provided convolution train model, in addition to a framework based on wavelet packets for simulating or learning such a process from multiple observations of disturbed input trains.