George Tsaklidis

The evolution of the attainable structures of a homogeneous Markov system by fixed size

In order to describe the evolution of the attainable structures of a homogeneous Markov system (HMS) with fixed size, we evaluate the volume of the sets of the attainable structures in Euclidean space as they are changing in time and we find the value of the volume asymptotically. We also estimate the evolution of the distance of two (attainable) structures of the system as it changes following the transformations of the structures; extensions are obtained concerning results from the PerronFrobenius theory referring to Markov systems. MANPOWER SYSTEMS; PERRON-FROBENIUS THEOREM AMS 1991 SUBJECT CLASSIFICATION: PRIMARY 90B70

Discrete Time Reward Models for Homogeneous Semi-Markov Systems

Abstract Previously, continuous time Markov and semi-Markow models have been developed for a multi-grade system with a number of transient states and a single absorbing state. Such systems have been studied with Poisson arrivals with known growth. Such models have been applied to manpower planning and the movement of patients through a hospital system. In this paper, we develop a reward model for a discrete time homogeneous semi-Markov system with Poisson arrivals and the same model where the system has growth with known size at each time point. Discrete time is employed here to accommodate a discrete reward structure. Results are obtained for the distribution, and mean of daily rewards of such system at any time, and in steady state; the expected reward in a period of time is also determined. These results are illustrated using data on employees moving through a company hierarchy and data for hospital patients.

Infinite Products of Matrices with Some Negative Elements and Row Sums Equal to One

Abstract Infinite products of a class of matrices, the V -matrices, with some negative elements and row sums equal to one are studied. After a series of lemmas and propositions, a basic theorem is provided where it is shown that the limit of an infinite product of V -matrices under certain conditions exists, Finally a method for finding this limit, based on some properties of generalized inverses, is provided.

Periodicity of infinite products of matrices with some negative elements and row sums equal to one

Abstract The problem of periodicity for the infinite products of a class of matrices, the V -matrices, with some negative elements and row sums equal to one is studied. After a series of lemmas, propositions, and theorems, a basic theorem is proved: that an infinite product of V -matrices under certain conditions splits into a number of subsequences which converge geometrically fast. Finally a method for finding these limits, based on some properties of generalized inverses, is provided.

Sensitivity analysis of market and stock returns by considering positive and negative jumps

Purpose This paper aims to present the results of further investigating the Polimenis (2012) stochastic model, which aims to decompose the stock return evolution into positive and negative jumps, and a Brownian noise (white noise), by taking into account different noise levels. This paper provides a sensitivity analysis of the model (through the analysis of its parameters) and applies this analysis to Google and Yahoo returns during the periods 2006-2008 and 2008-2010, by means of the third central moment of Nasdaq index. Moreover, the paper studies the behavior of the calibrated jump sensitivities of a single stock as market skew changes. Finally, simulations are provided for the estimation of the jump betas coefficients, assuming that the jumps follow Gamma distributions. Design/methodology/approach In the present paper, the model proposed in Polimenis (2012) is considered and further investigated. The sensitivity of the parameters for the Google and Yahoo stock during 2006-2008 estimated by means of the third (central) moment of Nasdaq index is examined, and consequently, the calibration of the model to the returns is studied. The associated robustness is examined also for the period 2008-2010. A similar sensitivity analysis has been studied in Polimenis and Papantonis (2014), but unlike the latter reference, where the analysis is done while market skew is kept constant with an emphasis in jointly estimating jump sensitivities for many stocks, here, the authors study the behavior of the calibrated jump sensitivities of a single stock as market skew changes. Finally, simulations are taken place for the estimation of the jump betas coefficients, assuming that the jumps follow Gamma distributions. Findings A sensitivity analysis of the model proposed in Polimenis (2012) is illustrated above. In Section 2, the paper ascertains the sensitivity of the calibrated parameters related to Google and Yahoo returns, as it varies the third (central) market moment. The authors demonstrate the limits of the third moment of the stock and its mixed third moment with the market so as to get real solutions from (S1). In addition, the authors conclude that (S1) cannot have real solutions in the case where the stock return time series appears to have highly positive third moment, while the third moment of the market is significantly negative. Generally, the positive value of the third moment of the stock combined with the negative value of the third moment of the market can only be explained by assuming an adequate degree of asymmetry of the values of the beta coefficients. In such situations, the model may be expanded to include a correction for idiosyncratic third moment in the fourth equation of (S1). Finally, in Section 4, it is noticed that the distribution of the error estimation of the coefficients cannot be considered to be normal, and the variance of these errors increases as the variance of the noise increases. Originality/value As mentioned in the Findings, the paper demonstrates the limits of the third moment of the stock and its mixed third moment with the market so as to get real solutions from the main system of equations (S1). It is concluded that (S1) cannot have real solutions when the stock return time series appears to have highly positive third moment, while the third moment of the market is significantly negative. Generally, the positive value of the third moment of the stock combined with the negative value of the third moment of the market can only be explained by assuming an adequate degree of asymmetry of the values of the beta coefficients. In such situations, the model proposed should be expanded to include a correction for idiosyncratic third moment in the fourth equation of (S1). Finally, it is noticed that the distribution of the error estimation of the coefficients cannot be considered to be normal, and the variance of these errors increases as the variance of the noise increases.

Correction to: Earthquake recurrence models and occurrence probabilities of strong earthquakes in the North Aegean Trough (Greece)

The original version of this article unfortunately contains mistakes. The mistakes and corrections are described in the following list: 1) Author names were incorrectly presented. The correct format is shown above as well as in the below affiliation section.

On the Convergence of the Discrete-Time Homogeneous Markov Chain

The evolution of a discrete-time Markov Chain (MC) is determined by the evolution equation p T (t) = p T (t − 1) · P, where p(t) stands for the stochastic state vector at time t, t∈ ℕ, P interprets the stochastic transition matrix of the MC, and the superscript Tdenotes transposition of the respective column vector (or matrix). The present chapter examines under which conditions concerning the stochastic matrix P, a set of stochastic vectors, { p(t − 1)}, representing a hypersphere on the set of the attainable structures of the MC, is transformed into a stochastic set { p(t) } also representing a hypersphere of the MC. The results concerning the form of the transition matrix Pare derived by means of the product PP T . The set of the matrices P turns out to be a subset of the set of the doubly stochastic matrices.

On a numerical approximation method of evaluating the interval transition probabilities of semi-Markov models

For the classical semi-Markov model, either time homogeneous or nonhomogeneous, an examination of the convergence of the interval transition probabilities pij(s,t) as t→∞ is presented using an approximation method provided by [R. De Dominics and R. Manca 1984]. Especially, we examined for various values of the step h the dependence of the accuracy of the respective numerical method in finding the transition interval probabilities and we investigated the complexity of this algorithm.

THE STRESS TENSOR OF THE CLOSED SEMI-MARKOV SYSTEM. ENERGY AND ENTROPY

The set of the attainable structures of a closed continuous time Homogeneous Semi-Markov System (HSMS) with n states, is considered as a continuum and the evolution of the HSMS in the Euclidean space E n corresponds to its motion. A suitable model of a continuum -for which the stress tensor depends on the acceleration gradient and the density-is proposed in order to explain the motion of the system. The adoption of this model enables us to establish the concept of the energy and the entropy of the HSMS.