Change detection in the Cox-Ingersoll-Ross model

We propose a change detection method for the famous Cox--Ingersoll--Ross model. This model is widely used in financial mathematics and therefore detecting a change in its parameters is of crucial importance. We develop one- and two-sided testing procedures for both drift parameters of the process. The test process is based on estimators that are motivated by the discrete time least-squares estimators, and its asymptotic distribution under the no-change hypothesis is that of a Brownian bridge. We prove the asymptotic weak consistence of the test, and derive the asymptotic properties of the change-point estimator under the alternative hypothesis of change at one point in time.Comment: 30 page

Change detection problems in branching processes

A sztochasztikus folyamatok paramétereinek megváltozását észlelni fontos statisztikai feladat, amely már az 1950-es évek óta kutatások tárgyát képezi. Ezek hagyományosan az autoregressziós folyamatra és egyéb klasszikus idősorokra koncentráltak, az elágazó folyamatok kevesebb figyelmet kaptak. Az értekezésben két igen hasonló, martingálelméleti alapokra épülő változásészlelési eljárást mutatunk be: először az egészértékű autoregressziós folyamatra (INAR(p)), amely a p-típusos elágazó folyamat speciális esete, majd a kamatlábmodellezésben használatos Cox-Ingersoll-Ross folyamatra, amely folytonos idejű, folytonos állapotterű elágazó folyamatként is ismert. Ebbe a sorba illeszkedik még egy harmadik eredmény is, amely az első két eljáráshoz hasonló gondolatokkal, a feltételes legkisebb négyzetek módszerét használva ad becslést a pénzügyi modellezésben elterjedt Heston-modell paramétereire diszkrét idejű megfigyelések alapján

Analog and digital modeling of sound and impaired periodontal supporting tissues during mechanical testing

Periodontitis is one of the most common conditions affecting oral health among adults, posing a great challenge for both patients and also for dentists aiming to treat this disease. In severe stages such deterioration of the supporting tissues, namely the periodontal ligaments and the bone, can occur, which will affect the biomechanical behavior and therefore the longevity and survival of the affected teeth. In order to be able to plan both periodontal and subsequent restorative treatment properly, valid modelling of the current clinical situation is advised. The aim of the present article is to comprehensively discuss possible analog and digital modeling methods of periodontally affected teeth and the periodontal structures surrounding them. Modelling possibilities can serve later as the basis of mechanical load, digital finite element studies, and also aid clinical treatment planning

Analog and digital modeling of sound and impaired periodontal supporting tissues during mechanical testing

Periodontitis is one of the most common conditions affecting oral health among adults, posing a great challenge for both patients and also for dentists aiming to treat this disease. In severe stages such deterioration of the supporting tissues, namely the periodontal ligaments and the bone, can occur, which will affect the biomechanical behavior and therefore the longevity and survival of the affected teeth. In order to be able to plan both periodontal and subsequent restorative treatment properly, valid modelling of the current clinical situation is advised. The aim of the present article is to comprehensively discuss possible analog and digital modeling methods of periodontally affected teeth and the periodontal structures surrounding them. Modelling possibilities can serve later as the basis of mechanical load, digital finite element studies, and also aid clinical treatment planning

Precision geoinformatical system of the pear gene-collection orchard

The principle task of the sustainable development is the preservation of the genetic variety, which is similar challenge in the horticulture regarding the sublimation of fruit species. The breeders of the traditional fruit strains give stock to the sustenance diversity of the agro-environment on the species and landscape level. In 2009, hyperspectral images have been taken by AISA Dual sensors from the pear gene pool in Újfehértó, Hungary. The hyperspectral data cube (in the wavelength range of 400-2500 nm, with 1.5 m ground resolution) ensured possibility to make the spectral library of pear species. In the course of the simultaneously field work the spatial position and individual extent of all pear trees was defined to set up a detailed GIS data base. The water stress sensitivity of single species and the descriptive spectral curves were determined with common evaluation of the spectral and spatial data. Based on the unique methodology processing and the hyperspectral data base suitable strains can be chosen for agro-environment and let take adaptive stocks regarding climate change into the genetic grafting work. Furthermore we could determine and map the sparsely species in the region with the help of the hyperspectral data

Analog and digital modeling of sound and impaired periodontal supporting tissues during mechanical testing

Periodontitis is one of the most common conditions affecting oral health among adults, posing a great challenge for both patients and also for dentists aiming to treat this disease. In severe stages such deterioration of the supporting tissues, namely the periodontal ligaments and the bone, can occur, which will affect the biomechanical behavior and therefore the longevity and survival of the affected teeth. In order to be able to plan both periodontal and subsequent restorative treatment properly, valid modelling of the current clinical situation is advised. The aim of the present article is to comprehensively discuss possible analog and digital modeling methods of periodontally affected teeth and the periodontal structures surrounding them. Modelling possibilities can serve later as the basis of mechanical load, digital finite element studies, and also aid clinical treatment planning

Defensive alliances in spatial models of cyclical population interactions

As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated and a neutral interacting partner. Depending on their interaction topologies, these systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. On three out of four cases three (or four) species form defensive alliances which maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate this mechanism results in an ordering phenomenon analogous to that of magnetic Ising model.Comment: 4 pages, 3 figure