The assessment of the risk connected to volcanic eruptions is a critical aspect when evaluating the safety of populated areas, either permanently or only temporarily, as it is the case for touristically attractive volcanoes. A stochastic approach has been developed for the analysis and simulation of data sampled at active volcanoes. This approach allows the detection of time correlation in the series, the statistical forecasts of volcanic events using Cox simulations and finally a volcanic tremor decomposition that can help identifying potential precursors preceding stronger eruptions. The described stochastic approach can be applied at very different time scales, therefore it may result useful for volcanoes as different as dormant ones and constantly active ones. In this presentation we concentrate mostly on the application of the method to data monitored at Stromboli volcano. Significant time correlation has been detected which leads one to describe Stromboli as a volcano with an exceptional memory of its recent past activity. Forecasting of the number of "normal" events for the next few days has been performed by Monte Carlo simulations. Finally, kriging of the time series derived from volcanic tremor intensity has enabled the extraction of time components, which could furnish additional monitoring variables for the forecast of paroxysmal phases at Stromboli. The use of different variables, either independently or together in a real multiparametric approach, is seen as a necessity in order to maximize the efficiency of such statistical monitoring tools.