scholarly journals Spatial components dependence for bidimensional time-constant AR(1) model with $$\alpha $$-stable noise and triangular coefficients matrix

2021 ◽  
Author(s):  
Aleksandra Grzesiek
Keyword(s):  
Time Series ◽  
Asymptotic Behaviour ◽  
Time Constant ◽  
Autoregressive Model ◽  
Asymptotic Relation ◽  
Autoregressive Time Series ◽  
One Dimensional ◽  
The Cross ◽  
The One ◽  
Stable Noise

AbstractIn this paper, we examine the bidimensional time-constant autoregressive model of order 1 with $$\alpha $$ α -stable noise. We focus on the case of the triangular coefficients matrix for which one of the spatial components of the model simplifies to the one-dimensional autoregressive time series. We study the asymptotic behaviour of the cross-codifference and the cross-covariation applied to describe the dependence in time between the spatial components of the model. As a result, we formulate the theorem about the asymptotic relation between both measures, which is consistent with the result that is correct for the case of the non-triangular coefficients matrix.

On the minimizers of the Ginzburg–Landau energy for high kappa: the one-dimensional case

1997 ◽  
Vol 8 (4) ◽  
pp. 331-345 ◽  
Author(s):  
AMANDINE AFTALION
Keyword(s):  
Magnetic Field ◽  
Asymptotic Behaviour ◽  
Dimensional Case ◽  
Numerical Computations ◽  
Ginzburg Landau ◽  
Landau Model ◽  
One Dimensional ◽  
Landau Parameter ◽  
Convergence Results ◽  
The One

The Ginzburg–Landau model for superconductivity is examined in the one-dimensional case. First, putting the Ginzburg–Landau parameter κ formally equal to infinity, the existence of a minimizer of this reduced Ginzburg–Landau energy is proved. Then asymptotic behaviour for large κ of minimizers of the full Ginzburg–Landau energy is analysed and different convergence results are obtained, according to the exterior magnetic field. Numerical computations illustrate the various behaviours.

scholarly journals Asymptotics for a parabolic double obstacle problem

1994 ◽  
Vol 444 (1922) ◽  
pp. 429-445 ◽  
Keyword(s):  
Asymptotic Behaviour ◽  
Obstacle Problem ◽  
Thin Strip ◽  
Normal Velocity ◽  
One Dimensional ◽  
Cahn Equation ◽  
Small Constant ◽  
The One ◽  
Short Time ◽  
Double Well Potential

We consider a parabolic double obstacle problem which is a version of the Allen-Cahn equation u t = Δ u — ϵ -2 ψ '( u ) in Ω x (0, ∞), where Ω is a bounded domain, ϵ is a small constant, and ψ is a double well potential; here we take ψ such that ψ ( u ) = (1 — u 2 ) when | u | ≤ 1 and ψ ( u ) = ∞ when | u | > 1. We study the asymptotic behaviour, as ϵ → 0, of the solution of the double obstacle problem. Under some natural restrictions on the initial data, we show that after a short time (of order ϵ 2 |ln ϵ |), the solution takes value 1 in a region Ω + t and value — 1 in Ω - t , where the region Ω ( Ω + t U Ω - t ) is a thin strip and is contained in either a O ( ϵ |ln ϵ |) or O ( ϵ ) neighbourhood of a hypersurface Γ t which moves with normal velocity equal to its mean curvature. We also study the asymptotic behaviour, as t → ∞, of the solution in the one-dimensional case. In particular, we prove that the ω -limit set consists of a singleton.

THE FINITE-DIFFERENCE METHOD OF ONE-DIMENSIONAL NONLINEAR SYSTEMS ANALYSIS

Fractals ◽  
2000 ◽  
Vol 08 (01) ◽  
pp. 49-65 ◽  
Author(s):  
A. YU. SHAHVERDIAN
Keyword(s):  
Time Series ◽  
Systems Analysis ◽  
Computational Study ◽  
Brain Activity ◽  
Logistic Map ◽  
Cantor Sets ◽  
Point Of View ◽  
One Dimensional ◽  
Time Flow ◽  
The One

The paper introduces one-dimensional analogy of Poincare "section" method. It reduces the one-dimensional nonlinear system orbit's study to consideration of some special conjugate orbit's "asymptotical" intersections with a thin arithmetical space of zero Lebesgue measure. The application of this approach to analysis of the logistic map orbits, earthquake time-series, and the sequences of fractional parts, is considered. Through computational study of these time-series, the existence of some Cantor sets, to which the conjugate orbits are attracted, is established. A fractal dynamical system, describing these different systems from a unified point of view, is introduced. The inner differential Cantorian structure of brain activity and time flow is discussed.

A new autoregressive time series model in exponential variables (NEAR(1))

1981 ◽  
Vol 13 (4) ◽  
pp. 826-845 ◽  
Author(s):  
A. J. Lawrance ◽  
P. A. W. Lewis
Keyword(s):  
Time Series ◽  
Autoregressive Model ◽  
Marginal Distribution ◽  
Sample Path ◽  
Cross Coupling ◽  
Time Series Model ◽  
Autoregressive Time Series ◽  
First Order ◽  
Joint Distributions ◽  
Two Parameter

A new time series model for exponential variables having first-order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (ear(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of directional effects in sample path behaviour. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and autocorrelations are investigated. A transformed version of the model has a uniform marginal distribution and its correlation and regression structures are also obtained. Estimation aspects of the models are briefly considered.

scholarly journals Rayleigh-Ritz variational method with suitable asymptotic behaviour

Open Physics ◽  
2014 ◽  
Vol 12 (8) ◽  
Author(s):  
Francisco Fernández ◽  
Javier Garcia
Keyword(s):  
Variational Method ◽  
Asymptotic Behaviour ◽  
Orthogonal Polynomial ◽  
Rate Of Convergence ◽  
Orthogonal Basis ◽  
Basis Sets ◽  
One Dimensional ◽  
Variational Calculations ◽  
Dimensional Models ◽  
The One

AbstractThis paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.

Convergence in Distribution of the One-Dimensional Kohonen Algorithms when the Stimuli are not Uniform

1994 ◽  
Vol 26 (1) ◽  
pp. 80-103 ◽  
Author(s):  
Catherine Bouton ◽  
Gilles Pagès
Keyword(s):  
Markov Chain ◽  
Probability Measure ◽  
Asymptotic Behaviour ◽  
Absolute Continuity ◽  
Invariant Probability Measure ◽  
Convergence In Distribution ◽  
One Dimensional ◽  
Open Set ◽  
Recurrent Markov Chain ◽  
The One

We show that the one-dimensional self-organizing Kohonen algorithm (with zero or two neighbours and constant step ε) is a Doeblin recurrent Markov chain provided that the stimuli distribution μ is lower bounded by the Lebesgue measure on some open set. Some properties of the invariant probability measure vε (support, absolute continuity, etc.) are established as well as its asymptotic behaviour as ε ↓ 0 and its robustness with respect to μ.

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