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Showing papers on "Asymptotology published in 2017"


Journal ArticleDOI
TL;DR: In this article, the asymptotic form of fixed-point solutions in functional truncations, in particular the f(R) approximation, has been studied both physically and mathematically.
Abstract: As already hinted at in Sect. 1.4.3, in order to understand fixed point solutions of the RG equation both physically and mathematically it is necessary to study their asymptotic behaviour. In this chapter we explain how to find the asymptotic form of fixed-point solutions in functional truncations, in particular the f(R) approximation.

53 citations


Book ChapterDOI
06 Sep 2017

49 citations


Journal ArticleDOI
TL;DR: In this paper, the existence and uniqueness of multi-order fractional differential equation systems were investigated and a representation of solutions of homogeneous linear MDFE systems in series form was provided.
Abstract: In this paper, we investigate some aspects of the qualitative theory for multi-order fractional differential equation systems. First, we obtain a fundamental result on the existence and uniqueness for multi-order fractional differential equation systems. Next, a representation of solutions of homogeneous linear multi-order fractional differential equation systems in series form is provided. Finally, we give characteristics regarding the asymptotic behavior of solutions to some classes of linear multi-order fractional differential equation systems.

35 citations


Book
08 Jun 2017
TL;DR: This paper provided a comprehensive account of asymptotic analysis of mixed effects models, including generalized linear mixed models, non-linear mixed effects, and non-parametric mixed effects.
Abstract: Large sample techniques are fundamental to all fields of statistics. Mixed effects models, including linear mixed models, generalized linear mixed models, non-linear mixed effects models, and non-parametric mixed effects models are complex models, yet, these models are extensively used in practice. This monograph provides a comprehensive account of asymptotic analysis of mixed effects models. The monograph is suitable for researchers and graduate students who wish to learn about asymptotic tools and research problems in mixed effects models. It may also be used as a reference book for a graduate-level course on mixed effects models, or asymptotic analysis.

20 citations


Posted Content
TL;DR: In this paper, the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein-Uhlenbeck process when a continuous record is available was obtained and an in-fill asymptotic theory for the least squares estimator was developed.
Abstract: This paper obtains the exact distribution of the maximum likelihood estimator of structural break point in the Ornstein-Uhlenbeck process when a continuous record is available The exact distribution is asymmetric, tri-modal, dependent on the initial condition These three properties are also found in the finite sam- ple distribution of the least squares (LS) estimator of structural break point in autoregressive (AR) models Motivated by these observations, the paper then develops an in-fill asymptotic theory for the LS estimator of structural break point in the AR(1) coefficient The in-fill asymptotic distribution is also asymmetric, tri-modal, dependent on the initial condition, and delivers excellent approximations to the finite sample distribution Unlike the long-span asymptotic theory, which depends on the underlying AR root and hence is tailor-made but is only available in a rather limited number of cases, the in-fill asymptotic theory is continuous in the underlying roots Monte Carlo studies show that the in-fill asymptotic theory performs better than the long-span asymptotic theory for cases where the long-span theory is available and performs very well for cases where no long-span theory is available

13 citations


Journal ArticleDOI
TL;DR: In this paper, a quantitative asymptotic, stability estimate for solutions to nonlinear evolution equations has been derived by measuring the distance in time of a solution to a parabolic problem.
Abstract: We study a quantitative asymptotic, stability estimates for solutions to nonlinear evolution equations. More precisely, we measure the distance in time of a solution to a parabolic problem from a solution to a stationary one.

12 citations


Journal ArticleDOI
TL;DR: For a general class of stationary random fields, asymptotic properties of the discrete Fourier transform (DFT), periodogram, parametric and nonparametric spectral density estimators under an easily verifiable short-range dependence condition expressed in terms of functional dependence measures were studied in this paper.
Abstract: For a general class of stationary random fields we study asymptotic properties of the discrete Fourier transform (DFT), periodogram, parametric and nonparametric spectral density estimators under an easily verifiable short-range dependence condition expressed in terms of functional dependence measures. We allow irregularly spaced data which is indexed by a subset $\Gamma $ of $\mathbb{Z}^{d}$. Our asymptotic theory requires minimal restriction on the index set $\Gamma $. Asymptotic normality is derived for kernel spectral density estimators and the Whittle estimator of a parameterized spectral density function. We also develop asymptotic results for a covariance matrix estimate.

10 citations


Posted Content
22 Jun 2017
TL;DR: In this paper, the fixed point index theory is applied to the Banach space to obtain fixed points of the integral operator in order to obtain solutions that satisfy some certain kind of asymptotic behavior.
Abstract: In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our knowledge, has never been used before. In order to obtain fixed points of the integral operator, we will consider the fixed point index theory and apply it to this new Banach space.

8 citations


13 Oct 2017
TL;DR: In this article, the authors studied the asymptotic behavior of global solutions to the initial value problem for the generalized KdV-Burgers equation and showed that the solution to this equation converges to a self-similar solution to the Burgers equation.
Abstract: We study the asymptotic behavior of global solutions to the initial value problem for the generalized KdV-Burgers equation. One can expect that the solution to this equation converges to a self-similar solution to the Burgers equation, due to earlier works related to this problem. Actually, we obtain the optimal asymptotic rate similar to those results and the second asymptotic profile for the generalized KdV-Burgers equation.

7 citations


Journal ArticleDOI
Yan Sun1
TL;DR: In this article, the authors developed asymptotic tests for the means of interval-valued population in the framework of random compact convex sets and derived analytical forms of the probability density functions for the limiting null distributions under both one-sample and two-sample settings.

6 citations


Journal Article
TL;DR: In this paper, the authors discuss the asymptotic behavior of solutions to higher-order Emden-Fowler type equations with constant potential and present a classification of all solutions.
Abstract: We discuss the asymptotic behavior of solutions to a higher-order Emden–Fowler type equation with constant potential. Several author’s results are presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities. We discuss the existence and asymptotic behavior of “blowup” solutions. Results on the asymptotic behavior of oscillating solutions are formulated. For the third- and forth-order equations an asymptotic classification of all solutions is presented. Some applications of the results obtained are proposed

Journal ArticleDOI
TL;DR: In this article, the authors consider hyperbolic equations with time-dependent coefficients and develop an abstract framework to derive the asymptotic behaviour of the representation of solutions for large times.

Journal ArticleDOI
TL;DR: In this article, an analogue of Vishik-Lyusternik-Vasileva-Imanalieva boundary functions method was proposed for constructing a uniform asymptotic expansion of solutions to many band bisingularly problems.
Abstract: The paper proposes an analogue of Vishik–Lyusternik–Vasileva–Imanalieva boundary functions method for constructing a uniform asymptotic expansion of solutions to many band (or with an intermediate boundary layers) bisingularly problems By means of this method we construct the uniform asymptotic expansion for the solution to the three-band bisingular Dirichlet problem for second order ordinary differential equation on the interval By the maximum principle we justify formal asymptotic expansion of the solution, that is, an estimate for the error term is established

Proceedings ArticleDOI
Yucai Zhu1
01 May 2017
TL;DR: In this article, an asymptotically globally convergent Box-Jenkins model estimation algorithm is proposed for black-box model identification and an error-in-variables model identification using over-sampling scheme.
Abstract: The so-called asymptotic theory of Ljung (1985) gives an error description of identified black-box model in the frequency domain. Based on the theory the asymptotic method of identification has been developed and applied successively in industrial MPC control and PID tuning. In this work, new results that extend the asymptotic theory and method will be presented: (1) an asymptotically globally convergent Box-Jenkins model estimation algorithm; (2) errors-in-variables model identification; and (3) accurate model identification using over-sampling scheme.

Journal ArticleDOI
05 May 2017
TL;DR: In this paper, an asymptotic approximation of the solution of the Cauchy problem for large times is constructed in the case where the initial function has a power-like asymPTotics at infinity.
Abstract: For the heat equation in the plane, an asymptotic approximation of the solution of the Cauchy problem for large times is constructed in the case where the initial function has a power-like asymptotics at infinity. In addition to direct application to heat conduction and diffusion processes, the study of the asymptotic behavior of the solution of the problem under consideration is of independent interest for the asymptotic analysis.

Journal ArticleDOI
TL;DR: Some new sufficient conditions for uniform global asymptotic stability for certain classes of nonlinear systems are established based on new nonlinear differential inequalities.
Abstract: In this paper, we establish some new sufficient conditions for uniform global asymptotic stability for certain classes of nonlinear systems. Lyapunov approach is applied to study exponential stability and stabilization of time-varying systems. Sufficient conditions are obtained based on new nonlinear differential inequalities. Moreover, some examples are treated and an application to control systems is given.

Proceedings ArticleDOI
01 Jul 2017
TL;DR: The aim is to find the slowest decaying solution, that is maximal asymptotic, for a class of first order linear differential equations given in infinite-dimensional space.
Abstract: We consider a class of first order linear differential equations given in infinite-dimensional space. We study asymptotic behavior of individual solutions in the context of stability. In particular, we are looking for the slowest decaying solution, that is maximal asymptotic. We present some new result on nonexistence of maximal asymptotics for certain class of linear equations.

Book ChapterDOI
01 Jan 2017
TL;DR: In this article, scaling and asymptotic analysis of the Navier-Stokes-Fourier system were used to eliminate unwanted or unimportant modes of motion, and to build in the essential balances between flow fields.
Abstract: The extreme generality of the full Navier-Stokes-Fourier system whereby the equations describe the entire spectrum of possible motions—ranging from sound waves, cyclone waves in the atmosphere, to models of gaseous stars in astrophysics—constitutes a serious defect of the equations from the point of view of applications. Eliminating unwanted or unimportant modes of motion, and building in the essential balances between flow fields, allow the investigator to better focus on a particular class of phenomena and to potentially achieve a deeper understanding of the problem. Scaling and asymptotic analysis play an important role in this approach. By scaling the equations, meaning by choosing appropriately the system of the reference units, the parameters determining the behavior of the system become explicit. Asymptotic analysis provides a useful tool in the situations when certain of these parameters called characteristic numbers vanish or become infinite.


Journal ArticleDOI
TL;DR: In this paper, the uniqueness result of the LDA model in stationary and transitory cases and in one dimensional space has been shown in a one-dimensional space and in time.

Posted Content
TL;DR: In this paper, the asymptotic stability of the equilibrium points in the Landau-Lifshitz equation is established and a suitable Lyapunov function is presented.
Abstract: The Landau--Lifshitz equation describes the behaviour of magnetic domains in ferromagnetic structures. Recently such structures have been found to be favourable for storing digital data. Stability of magnetic domains is important for this. Consequently, asymptotic stability of the equilibrium points in the Landau--Lifshitz equation are established. A suitable Lyapunov function is presented.

Journal ArticleDOI
10 Jan 2017
TL;DR: In this paper, the authors deal with the dynamics of the solutions to the system of second order nonlinear difference equations, where A ∈ (0,∞), B ∈ 0, 1, ∞, x−i ∈ 1, 2 ∈ 2, 3 ∞ and y−I ∈ 3, 4 ∞.
Abstract: This paper deals with dynamics of the solutions to the system of second order nonlinear difference equations xn+1 = xn A+ ynyn−1 , yn+1 = yn B + xnxn−1 , n = 0, 1, · · · , where A ∈ (0,∞), x−i ∈ (0,∞), y−i ∈ (0,∞), i = 0, 1. Moreover we use the known results to determine the rate of convergence of the solutions of this system. Finally, we give some numerical examples to justify our results.

Journal ArticleDOI
TL;DR: In this article, a singularly perturbed boundary-value problem for an equation of mixed ellipticparabolic type is considered and an effective numerical algorithm based on an asymptotic representation of the solution is developed.
Abstract: A singularly perturbed boundary-value problem for an equation of mixed ellipticparabolic type is considered. The first part of this work is devoted to an asymptotic study of the solution to the problem. Modification of the boundary function method for mixed-type equations with small parameters at the highest derivatives is used. The second part is devoted to creating a numerical method that considers the structure of the solution for small parameter values. The idea of an approximate factorization of an elliptic operator into the product of two parabolic operators is employed. An effective numerical algorithm based on an asymptotic representation of the solution is developed.

Proceedings ArticleDOI
21 Jul 2017
TL;DR: In this article, the authors considered a class of nonlocal systems of reaction-diffusion equations with coefficients which are Lipschitz-continuous positive functions and designed a coupling technique consisting of the non-standard finite difference (NSFD) and finite element method (FEM) both in time and space respectively.
Abstract: This paper is considered on a class of nonlocal systems of reaction-diffusion equations with coefficients which are Lipschitz-continuous positive functions. In this model, we are concerned with designing a coupling technique consisting of the non-standard finite difference(NSFD) and finite element method(FEM) both in time and space respectively. We prove theoretically that the schemes designed by the above technique converges optimally in some specified norms for given conditions. Furthermore, we show that the numerical solutions of the said schemes replicates the decaying properties of the exact solutions. Numerical experiments are presented to justify the above theory and some practical studies are carried out for the asymptotic behavior of the schemes under consideration.

Journal ArticleDOI
TL;DR: In this article, the authors obtain integral inequalities of Stieltjes type, and apply the inequalities to the study of asymptotic behavior of a certain second-order integrodifferential equation.
Abstract: Differential equations arise in various real world phenomena in mathematical physics, mechanics, engineering, biology and so on. Also integral inequalities are very useful tools in global existence, uniqueness, stability and other properties of the solutions of various nonlinear differential equations, see, e.g., [6, 7]. In this paper, we obtain some integral inequalities of Stieltjes type, and apply the inequalities to the study of asymptotic behavior of a certain second-order integrodifferential equation. The asymptotic behaviors of various second-order nonlinear differential equations have been studied by many authors, see, e.g., [5, 8] and the references cited there.