Likelihood functions for multivariate point processes with coincidences.

Existing work on scalar and multivariate point process models assumes a no-simultaneity condition i.e. no more than one event of any kind can occur in a small time interval. But there is now strong interest from a number of fields such as neuro-physiology in being able to construct models that allow simultaneity. Here we construct such models and associated likelihood (ratios) for the first time.