Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: Conditions of the boundedness of the solutions, stability in the first approximation, and asymptotic equivalence for discrete Volterra-type equations are proven.
Abstract: Conditions of the boundedness of the solutions, stability in the first approximation, and asymptotic equivalence for discrete Volterra-type equations are proven. All are formulated in terms of the characteristics of the equations, using an operator approach.
5 citations
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TL;DR: This paper provides a personal overview of the local asymptotic normality (LAN) results for linear processes, nonlinear processes, diffusion processes, long-memory processes, and locally stationary processes, etc..
Abstract: The local asymptotic normality (LAN) , introduced by LeCam, is the most fundamental concept in the statistical asymptotic theory. If LAN property for a class of statistical models is established, then the asymptotic optimality of estimator and test can be described in terms of the central sequence. This concept gives a unified view for the statistical estimation and testing theory. Recently the LAN concept has been introduced to the asymptotic theory for time series. This paper provides a personal overview of the LAN results for linear processes, nonlinear processes, diffusion processes, long-memory processes, and locally stationary processes, etc.. The results are applied to the asymptotic estimation, testing theory, and discriminant analysis in time series. Then, construction of asymptotically optimal estimator, test and discriminator is discussed.
5 citations
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TL;DR: In this paper, the authors revisited the asymptotic convergence properties of the 3D-shell model with respect to the thickness parameter and established strong convergence results for the model in bending-and membrane-dominated behavior.
Abstract: We revisit the asymptotic convergence properties—with respect to the thickness parameter—of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong convergence results for the 3D-shell model in the two main types of asymptotic regimes, namely, bending- and membrane-dominated behavior. This is an important achievement, as it completely substantiates the asymptotic consistency of the 3D-shell model with 3D linearized isotropic elasticity.
5 citations
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TL;DR: In this paper, the authors developed an approach based on state asymptotic estimator for distributed diffusion F-systems, where the dynamical systems are uncontrolled (Fsystems).
Abstract: The aim of this paper is to develop an approach based on state asymptotic estimator. More precisely, we extend the notion of regional asymptotic observability as in ref. [1] to the case where the dynamical systems are uncontrolled (Fsystems). For different sensors, we give the characterizations of regional asymptotic free observer in order that asymptotic free observability can be achieved. Furthermore, we show that, there exists a dynamical F-system for distributed diffusion F-system is not asymptotic F-observable in the usual sense, but it may be regional asymptotic Fobservable.
5 citations
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01 Jan 1995TL;DR: In this article, a generalization of Levy walk in one dimension allowing for an arbitrary bias and asymmetry of jumps is proposed, where an asymptotic distribution of distance R(t) reached up to time t by a particle initially at the origin is found to be a possibly asymmetric Levy-stable law s α,β (τ) or a positive law hλ(xx).
Abstract: We propose a generalization of Levy walk in one dimension allowing for an arbitrary bias and asymmetry of jumps. An asymptotic distribution (propagator) of distance R(t) reached up to time t by a particle initially at the origin is found to be a possibly asymmetric Levy-stable law s α,β (τ) or a positive law hλ(xx). A probabilistic approach in terms of random variables R; and T i is applied.
4 citations