Using spatial Markovian chain for the statistical analysis of seismic occurrences in the Azores Region

The objective of this paper is to study the spatial sequence of the epicentral locations of seismic occurrences (Space variable) in the Azores region. In a previous investigation based on geological considerations and statistical criteria that addresses the existing historical and instrumental information, the epicentral locations were assigned to seven seismic zones. This paper focuses on the analysis of occurrences in the seven seismic zones using Markovian chains. The probability of occurrence of an earthquake in one of the seven adopted zones is estimated, revealing great differences among the seismic zones. Additionally, the one-step transitions of this variable (seismic zone for the next occurrence in time) are explored and show an evident dependence between consecutive earthquake locations. Assuming that the process is stationary, N-step transitions are also discussed. Based on the developed Markovian model, this study also simulates the sequence of epicentral zones where occurrences can take place, which is an important component of modelling the entire process of seismic occurrences in the Azores region.

Problem of Kolmogorov for Markovian chains

The sums of random variables from two-state Markovian chain in the schemes of series are investigated. The sums are approximated by parametrical set of measures, which is constituted by all possible limitmeasures of such sums, after making discrete in continuous cases. The problem of Kolmogorov is under solution: the accuracy of approximation by the most relevant measure from parametrical set is evaluated interms of metrics of variation. The common solution scheme of Kolmogorovæs problem is described and the final results for one particular parametrical measure are presented.