Calculation of seismic risks in a zone are based on stochastic models describing at best the seismic activity. Our focus is the spatio-temporal evolution of the probability of earthquake occurrences. The main modelling tool is the theory of the point processes. We discuss about the spatio-temporal extension of ETAS (Epidemic Type Aftershock Sequence) with marks and study the properties of the log-likelihood and the maximum likelihood estimators. Seismic data from the Lesser Antilles Arc carried out between 1999 and 2004 are analyzed.