Levy Approximation of Impulsive Recurrent Process with Semi-Markov Switching

In this paper, the weak convergence of impulsive recurrent process with semi-Markov switching in the scheme of Levy approximation is proved. Singular perturbation problem for the compensating operator of the extended Markov renewal process is used to prove the relative compactness

A semi-Markov model with memory for price changes

We study the high frequency price dynamics of traded stocks by a model of returns using a semi-Markov approach. More precisely we assume that the intraday returns are described by a discrete time homogeneous semi-Markov which depends also on a memory index. The index is introduced to take into account periods of high and low volatility in the market. First of all we derive the equations governing the process and then theoretical results have been compared with empirical findings from real data. In particular we analyzed high frequency data from the Italian stock market from first of January 2007 until end of December 2010

Pathwise Sensitivity Analysis in Transient Regimes

The instantaneous relative entropy (IRE) and the corresponding instanta- neous Fisher information matrix (IFIM) for transient stochastic processes are pre- sented in this paper. These novel tools for sensitivity analysis of stochastic models serve as an extension of the well known relative entropy rate (RER) and the corre- sponding Fisher information matrix (FIM) that apply to stationary processes. Three cases are studied here, discrete-time Markov chains, continuous-time Markov chains and stochastic differential equations. A biological reaction network is presented as a demonstration numerical example

False-negative results using Neisseria gonorrhoeae porA pseudogene PCR - a clinical gonococcal isolate with an N. meningitidis porA sequence, Australia, March 2011

The gonococcal porA pseudogene is a popular target for in-house Neisseria gonorrhoeae PCR methods. With this study we present two novel findings: the first case of an N. gonorrhoeae porA pseudogene PCR false-negative result caused by sequence variation, and in the same organism, the first description of a clinical N. gonorrhoeae strain harbouring an N. meningitidis porA sequence

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

MODELING THE SEISMICITY OF CENTRAL IONIAN ISLANDS WITH SEMI-MARKOV MODELS

Ένας κατάλογος σεισμών μεγέθους M ≥ 5.2, οι οποίοι έγιναν από το 1911 ως το 2014 στην περιοχή του κεντρικού Ιονίου, θα θεωρηθεί ότι αποτελεί μια ημι Μαρκοβιανή αλυσίδα, αποσκοπώντας στην εκτίμηση της σεισμικής επικινδυνότητας. Θα υποθέσουμε ότι οι ενδιάμεσοι χρόνοι (χρόνοι μεταξύ των σεισμών) ακολουθούν γεωμετρικές κατανομές ή προσεγγίζονται από κατανομές Pareto. Οι υπό μελέτη ποσότητες είναι οι πιθανότητες προορισμού (destination probabilities). Σε αρκετές περιπτώσεις διαπιστώθηκε ότι οι πιθανότητες αυτές λαμβάνοντας μεγαλύτερη τιμή, προβλέπουν σωστά την κατηγορία μεγέθους του επόμενου σεισμού. Επίσης, το μοντέλο με γεωμετρικούς ενδιάμεσους χρόνους μπορεί να χρησιμοποιηθεί και για να υποδείξει τον αναμενόμενο χρόνο του επόμενου σεισμού, καθώς το ποσοστό της επιτυχούς εκτίμησης του χρόνου είναι 63.75% για όλους τους υπό μελέτη σεισμούς ενώ γίνεται 71.42% όσον αφορά τους μεγαλύτερους σεισμούς (M ≥ 6.0).Earthquakes with M ≥ 5.2 that occurred in the area of central Ionian Islands (1911- 2014) are assumed to form a semi-Markov chain, aiming to contribute in the field of seismic hazard assessment. The sojourn times are considered to be geometric or approximated by Pareto distributions. Destination probabilities are examined and the results demonstrate that in many cases these probabilities become higher adequately forecasting the magnitude class of an anticipated earthquake. The geometrically distributed model can also reveal the more probable occurrence time of the next earthquake since for this model the destination probabilities were found to obtain many times their maximum values for the real occurrence time. The successful forecasting as for the occurrence time is 63.75% for all earthquakes and becomes 71.42% for the larger magnitude events (M ≥ 6.0)