SEMI-MARKOV MODELS FOR SEISMIC HAZARD ASSESSMENT IN CERTAIN AREAS OF GREECE

The long-term probabilistic seismic hazard is studied through the application of semi-Markov model. In this model a sequence of earthquakes is considered as a Markov process and the waiting time distributions depend only on the type of the last and the next event. The principal hypothesis of the model is the property of one-step memory, according to which the probability of moving to any future state depends only on the present state. The model under consideration defines a continuous-time, discrete-state stationary process in which successive state occupancies are governed by the transition probabilities of the Markov process. The space of states is considered to be finite and the process started far in the past has achieved stationarity. Firstly, a non-parametric method is applied in order to determine the waiting times. Then, the waiting times derived by means of the exponential and Weibull distributions will be compared to each other, as well as with the actual waiting times. Thus, the probability of occurrence of the anticipated earthquakes of a specific magnitude scale is calculated. The models are applied to an historical catalogue for Northern Aegean Sea

Development of a Reference Wafer for On-Wafer Testing of Extreme Impedance Devices

This paper describes the design, fabrication, and testing of an on-wafer substrate that has been developed specifically for measuring extreme impedance devices using an on-wafer probe station. Such devices include carbon nano-tubes (CNTs) and structures based on graphene which possess impedances in the κ Ω range and are generally realised on the nano-scale rather than the micro-scale that is used for conventional on-wafer measurement. These impedances are far removed from the conventional 50- reference impedance of the test equipment. The on-wafer substrate includes methods for transforming from the micro-scale towards the nano-scale and reference standards to enable calibrations for extreme impedance devices. The paper includes typical results obtained from the designed wafer

A Markov model for seismic hazard analysis along the Hellenic subduction Zone (Greece)

Εφαρμόζεται  ένα  ομογενές  Μαρκοβιανό  μοντέλο  διακριτού  χρόνου  και  χώρου καταστάσεων για τη γένεση σεισμών στο Ελληνικό Τόξο, περιοχή υψηλής σεισμικής δραστηριότητας  και  ιδιαίτερης  σημασίας  από  σεισμοτεκτονική  άποψη.  Το  μοντέλο παρέχει μια στοχαστική αναπαράσταση της γένεσης των σεισμών συμβάλλοντας στην εκτίμηση της σεισμικής επικινδυνότητας για την περιοχή μελέτης. Τα δεδομένα που χρησιμοποιούνται  λήφθηκαν  από  τον  κατάλογο  του  Τομέα  Γεωφυσικής  του Αριστοτελείου  Πανεπιστημίου  Θεσσαλονίκης,  ο  οποίος  θεωρείται  ομογενής  και  πλήρης  για  σεισμούς  με  από  το  1911.  Ο  συνεχής  χώρος  καταστάσεων χωρίζεται  σε  κλάσεις  μεγεθών  καθορίζοντας  με  αυτό  τον  τρόπο  τον  χώρο καταστάσεων  του  μοντέλου.  Η  στοχαστική  συμπεριφορά  του  μοντέλου  καθορίζεται XLVII, No 3 - 1376από  τον  πίνακα  πιθανοτήτων  μετάβασής  του,  του  οποίου  υπολογίζεται  αρχικά ο εκτιμητής   μέγιστης   πιθανοφάνειας.   Στη  συνέχεια   εκτιμώνται   σημαντικά χαρακτηριστικά της Μαρκοβιανής αλυσίδας, παρέχοντας προγνωστικά αποτελέσματα σχετικά  με  την  πιθανότητα  γένεσης  ενός  επερχόμενου  ισχυρού  σεισμού.  Οι υπολογισμοί  περιλαμβάνουν  την  εκτίμηση  της  μέσης  τιμής,  της  διασποράς  και  του 95% διαστήματος εμπιστοσύνης του πλήθους των βημάτων που απαιτούνται ώστε η Μαρκοβιανή αλυσίδα να μεταβεί για πρώτη φορά σε μια ορισμένη κατάσταση (που σχετίζεται με τη γένεση ενός επερχόμενου ισχυρού σεισμού).A homogeneous finite–state discrete–time Markov model is applied for the earthquake occurrence in the Hellenic Subduction Zone (Greece), a region accommodating high seismic activity, being a key structure from a seismotectonic point of view. An attempt is made to provide a stochastic representation of the earthquake process and to assess the seismic hazard through the application of the Markov model. The model is applied on a complete data sample comprising strong () eart  h-quakes that occurred in the study area since 1911 up to present. The continuous magnitude scale is divided into appropriate intervals to specify discrete states of the model. As the stochastic behavior of the model is governed by its transition probability matrix, we firstly estimate its well–known maximum likelihood estimator. The estimation of the transition probability matrix leads to the estimation of important indicators of the Markov chain, including hitting times and failure rate functions. The   mean number of steps for the first occurrence of an anticipated earthquake (belonging to the class with the stronger events, which we are more interested in) is estimated along with its variance. In a next step, we calculate the confidence interval of the   aforementioned estimators

Hypotheses testing and posterior concentration rates for semi-Markov processes

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Hypotheses testing and posterior concentration rates for semi-Markov processes

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and finite state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates

Hypotheses testing and posterior concentration rates for semi-Markov processes

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and finite state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates