Search

In this paper, we introduce and study the Power Periodic Threshold GARCH Model (PPTGARCH). We give the necessary and sufficient conditions for the existence of the unique strictly periodically stationary solution of the model and the necessary and sufficient conditions for the existence of moments. A sufficient condition for the periodic geometric ergodicity and β – mixing property using the uniform countable additivity condition is given. We prove the consistency and asymptotic normality of the Quasi-Maximum Likelihood estimator (QMLE) of the parameters. Simulation studies to illustrate consistency and asymptotic normality of the estimators for different underlying error distributions are presented. [ABSTRACT FROM AUTHOR]

This article investigates the problem of the definition and computation of anH2-type norm for discrete-time time-varying periodic stochastic linear systems simultaneously affected by multiplicative white noise perturbations and random jumping according to a Markov chain with an infinite countable number of states. Also, we solve an optimization problem that contains, as a special case, theH2optimal control problem for the considered class of stochastic systems under the assumption of perfect state measurements. [ABSTRACT FROM AUTHOR]

We use a new nonlinear method to study linear difference equations with variable coefficients in a non-trivial ringR. If the homogeneous part of the linear equation has a solution in the unit group of a ring with identity (a unitary solution), then we show that the equation decomposes into two linear equations of lower orders. This decomposition, known as a semiconjugate factorization in the nonlinear theory, is based on sequences of ratios of consecutive terms of a unitary solution. Such sequences, which may be called eigensequences, are well suited to variable coefficients; for instance, they provide a natural context for the expression of the Poincaré–Perron theorem. As applications, we obtain new results for linear difference equations with periodic coefficients and for linear recurrences in rings of functions (e.g. the recurrence for the modified Bessel functions). [ABSTRACT FROM PUBLISHER]

We extend the known results of the non-autonomous difference equationto the situation where (i) the parameters βn, γn,AnandBnare period-two sequences of non-negative real numbers with γnnot identically zero andAn+Bn ≠ 0 and (ii) the initial conditionsx− 1andx0are such thatand. [ABSTRACT FROM AUTHOR]

Patterns of contact in social behaviour and seasonality due to environmental influences often affect the spread and persistence of diseases. Models of epidemics with seasonality and patterns in the contact rate include time-periodic coefficients, making the systems nonautonomous. No general method exists for calculating the basic reproduction number, the threshold for disease extinction, in nonautonomous epidemic models. However, for some epidemic models with periodic coefficients and constant population size, the time-averaged basic reproduction number has been shown to be a threshold for disease extinction. We extend these results by showing that the time-averaged basic reproduction number is a threshold for disease extinction when the population demographics are periodic. The results are shown to hold in epidemic models with periodic demographics that include temporary immunity, isolation, and multiple strains. [ABSTRACT FROM AUTHOR]

We present global convergence results related to periodically forced rational difference equations. [ABSTRACT FROM AUTHOR]

We study global attractivity of the period-two coefficient version of the delay logistic difference equation, also known as Pielou's equation,[image omitted] where[image omitted] We prove that for [image omitted] , zero is the unique equilibrium point. If [image omitted] , then zero is globally asymptotically stable, with basin of attraction given by the nonnegative quadrant of initial conditions. If [image omitted] , then zero is unstable, and a sequence [image omitted] converges to zero if and only if [image omitted] . If [image omitted] , then the sequence [image omitted] converges to the unique period-two solution[image omitted] where [image omitted] and [image omitted] are uniquely determined by the equations[image omitted] [ABSTRACT FROM AUTHOR]

We investigate the trichotomy character and the global asymptotic stability of solutions of the difference equation in the title where any of the parameters are a period-two sequence with non-negative values and the initial conditions are positive. [ABSTRACT FROM AUTHOR]

We investigate the periodic nature, the boundedness character and the global asymptotic stability of solutions of the difference equation [This symbol cannot be presented in ASCII format] where the parameter pn is a period-two sequence with positive values and the initial conditions are positive. [ABSTRACT FROM AUTHOR]