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Due to the complexity of the generator process of seismic events, westudy under several aspects the interaction structure between earthquake events usingrecently developed spatio-temporal statistical techniques and models. Usingthese advanced statistical tools, we aim to characterise the global and local scalecluster behaviour of the Easter Sicily seismicity considering the catalogue datasince 2006, when the Italian National Seismic Network was upgraded and earthquakelocation was sensibly improved. Firstly, we characterise the global complexspatio-temporal interaction structure with the space-time ETAS model where backgroundseismicity is estimated non-parametrically, while triggered seismicity is estimatedby MLE. After identifying seismic sequences by a clustering technique, wecharacterise their spatial and spatio-temporal interaction structures using advancedpoint process models. For the characterisation of the spatial interactions, a versionof hybrid of Gibbs point process models is proposed as method to characterise themultiscale interaction structure of several seismic sequences accounting both forthe attractive and repulsive nature of data. Furthermore, we consider log-GaussianCox processes (LGCP), that are relatively tractable class of empirical models fordescribing spatio-temporal correlated phenomena. Several parametric formulationof spatio-temporal LGCP are estimated, by the minimum contrast procedure, assumingboth separable and non-separable parametric specification of the correlationfunction of the underlying Gaussian Random Field.