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Large and Moderate Deviations for Projective Systems and Projective Limits

Applied Mathematics 2012年第12期3卷 2041-2047页

作者： tryfon daras Department of Sciences Technical University of Crete Chania Greece

One of the active fields in applied probability, the last two decades, is that of large deviations theory i.e. the one dealing with the (asymptotic) computation of probabilities of rare events which are exponentially small as a function of some parameter e.g. the amplitude of the noise perturbing a dynamical system. Basic ideas of the theory can be tracked back to Laplace, the first rigorous results are due to Cramer although a clear definition was introduced by Varadhan in 1966. Large deviations estimates have been proved to be the crucial tool in studying problems in Statistics, Physics (Thermodynamics and Statistical Mechanics), Finance (Monte-Carlo methods, option pricing, long term portfolio investment) and in Applied probability (queuing theory). The aim of this work is to describe one of the (recent) methods of proving large deviations results, namely that of projective systems. We compare the method with the one of projective limits and show the advantages of the first. These advantages are due to the fact that: 1) the arguments are direct and the proofs of the basic results of the theory are much easier and simpler;2) we are able to extend most of these results using suitable projective systems. We apply the method in the case of a) sequences of i.i.d. r.v.’s and b) sequences of exchangeable r.v.’s. All the results are being proved in a simple “unified” way.

关键词： Large Deviations Projective Systems Projective Limits Moderate Deviations

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A Novel Heuristic Algorithm for theModeling and Risk Assessment of the COVID-19 Pandemic Phenomenon

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Computer Modeling in Engineering & Sciences 2020年第11期125卷 815-828页

作者： Panagiotis G.Asteris Maria G.Douvika Chrysoula A.Karamani Athanasia D.Skentou Katerina Chlichlia Liborio Cavaleri tryfon daras Danial J.Armaghani Theoklis E.Zaoutis Computational Mechanics Laboratory School of Pedagogical and Technological EducationAthens15122Greece Laboratory of Molecular Immunology Department of Molecular Biology and GeneticsDemocritus University of ThraceAlexandroupolisGreece Department of Civil EnvironmentalAerospace and Materials EngineeringUniversity of PalermoPalermoItaly School of Environmental Engineering Technical University of CreteChaniaGreece Department of Civil Engineering Faculty of EngineeringUniversity of MalayaKuala LumpurMalaysia Division of Infectious Diseases The Children’s Hospital of PhiladelphiaPerelman School of MedicineUniversity of PennsylvaniaPHLUSA

Themodeling and risk assessment of a pandemic phenomenon such as COVID-19 is an important and complicated issue in epidemiology,and such an attempt is of great interest for public health *** this end,in the present study,based on a recent heuristic algorithm proposed by the authors,the time evolution of COVID-19 is investigated for six different countries/states,namely New York,California,USA,Iran,Sweden and *** number of COVID-19-related deaths is used to develop the proposed heuristic model as it is believed that the predicted number of daily deaths in each country/state includes information about the quality of the health system in each area,the age distribution of population,geographical and environmental factors as well as other *** on derived predicted epidemic curves,a new 3D-epidemic surface is proposed to assess the epidemic phenomenon at any time of its *** research highlights the potential of the proposed model as a tool which can assist in the risk assessment of the *** its development through 3D-epidemic surface can assist in revealing its dynamic nature as well as differences and similarities among different districts.

关键词： Algorithm COVID-19 Gaussian-function heuristic model pandemic trend prediction SARS-CoV-2

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