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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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Book
29 Jan 2014
TL;DR: In this article, the authors present a broad overview of local asymptotics for statistical experiments in the sense of mixed normality or local Asymptotic quadraticity.
Abstract: This textbook is devoted to the general asymptotic theory of statistical experiments. Local asymptotics for statistical models in the sense of local asymptotic (mixed) normality or local asymptotic quadraticity make up the core of the book. Numerous examples deal with classical independent and identically distributed models and with stochastic processes.

22 citations

Journal ArticleDOI
TL;DR: In this paper, an elliptic self-adjoint first order pseudodifferential operator acting on columns of complex-valued half-densities over a connected compact manifold without boundary is considered.
Abstract: We consider an elliptic self-adjoint first order pseudodifferential operator acting on columns of complex-valued half-densities over a connected compact manifold without boundary. The eigenvalues of the principal symbol are assumed to be simple but no assumptions are made on their sign, so the operator is not necessarily semi-bounded. We study the following objects: the propagator (time-dependent operator which solves the Cauchy problem for the dynamic equation), the spectral function (sum of squares of Euclidean norms of eigenfunctions evaluated at a given point of the manifold, with summation carried out over all eigenvalues between zero and a positive lambda) and the counting function (number of eigenvalues between zero and a positive lambda). We derive explicit two-term asymptotic formulae for all three. For the propagator "asymptotic" is understood as asymptotic in terms of smoothness, whereas for the spectral and counting functions "asymptotic" is understood as asymptotic with respect to lambda tending to plus infinity.

21 citations

Journal ArticleDOI
TL;DR: The aim of this paper is to construct some asymptotic expansions which produce increasingly accurate approximations of the gamma function.
Abstract: The aim of this paper is to construct some asymptotic expansions which produce increasingly accurate approximations of the gamma function.

21 citations

Journal Article
TL;DR: In this article, the stability of a class of linear systems including gamma-distributed delay with a gap is studied. And a complete characterization of stability regions is given in the corresponding (delay, mean-delay) parameter space.
Abstract: This paper focuses on the stability of a class of linear systems including gamma-distributed delay with a gap. More precisely, a complete characterization of stability regions is given in the corresponding (delay, mean-delay) parameter-space. Optimal delay intervals are explicitly computed. The stabilizing/destabilizing delay effect will be explicitly outlined, and discussed. Several illustrative examples complete the paper.

21 citations

Journal ArticleDOI
TL;DR: Based on the asymptotic distribution of quadratic form in Gaussian random variables, two formulations for the case when the number of random variables n→∞ is provided are proposed, which result in simple closed-form expressions for the probability of failure of an engineering structure.
Abstract: In the reliability analysis of safety critical complex engineering structures, a very large number of the system parameters can be considered as random variables. The difficulty in computing the failure probability using the classical first- and second-order reliability methods (FORM and SORM) increases rapidly with the number of variables or ‘dimension’. There are mainly two reasons behind this. The first is the increase in computational time with the increase in the number of random variables. In principle, this problem can be handled with superior computational tools. The second reason, which is perhaps more fundamental, is that there are some conceptual difficulties typically associated with high dimensions. This means that even when one manages to carry out the necessary computations, the application of existing FORM and SORM may still lead to incorrect results in high dimensions. This paper is aimed at addressing this issue. Based on the asymptotic distribution of quadratic form in Gaussian random variables, two formulations for the case when the number of random variables n/N is provided. The first is called ‘strict asymptotic formulation’ and the second is called ‘weak asymptotic formulation’. Both approximations result in simple closed-form expressions for the probability of failure of an engineering structure. The proposed asymptotic approximations are compared with existing approximations and Monte Carlo simulations using numerical examples.

21 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526