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Campi Flegrei (CF) is a densely urbanized caldera with a very high volcanic risk. Its more recent volcanic activity was characterized in the last 15 kyrs by more than 70 explosive events of variable scale and vent location. The sequence of eruptive events at CF is remarkably inhomogeneous, both in space and time. Eruptions concentred over periods from a few centuries to a few millennia, and were alternated by periods of quiescence lasting up to several millennia. As a consequence, activity has been subdivided into three distinct epochs, i.e. Epoch I, 15- 9.5 kyrs, Epoch II, 8.6 - 8.2 kyrs, and Epoch III, 4.8 - 3.7 kyrs BP [e.g. Orsi et al., 2004; Smith et al., 2011]. The eruptive record also shows the presence of clusters of events in space-time, i.e. the opening of a new vent in a particular location and at a specific time seems to increase the probability of another vent opening in the nearby area and in the next decades-centuries (self-exciting effect). Probabilistic vent opening mapping conditional the occurrence of a new event and able to account for some of the intrinsic uncertainties affecting the system, has been investigated in some recent studies [e.g. Selva et al. 2011, Bevilacqua et al. 2014, in preparation], but a spatial-temporal model of the sequence of volcanic activity remains an open issue. Hence we have developed a time-space mathematical model that takes into account both the self-exciting behaviour of the system and the significant uncertainty affecting the eruptive record. Based on the past eruptive record of the volcano, the model allows to simulate sequences of future events as well as to better understand the spatial and temporal …