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: Asymptotic properties of bias-corrected estimators for small diffusion models from the viewpoint of information geometry were investigated in this article, where the authors obtained results analogous to those for independent and identically distributed (iid) models.
Abstract: Information geometrical quantities such as metric tensors and connection coefficients for small diffusion models are obtained Asymptotic properties of bias-corrected estimators for small diffusion models are investigated from the viewpoint of information geometry Several results analogous to those for independent and identically distributed (iid) models are obtained by using the asymptotic normality of the statistics appearing in asymptotic expansions In contrast to the asymptotic theory for iidmodels, the geometrical quantities depend on the magnitude of noise
1 citations
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TL;DR: In this paper, the authors combine the method of multiple scales and the matched asymptotic expansions to construct uniformly-valid solutions to autonomous and non-autonomous difference equations in the neighbourhood of a period-doubling bifurcation.
Abstract: In this paper, we combine the method of multiple scales and the method of matched asymptotic expansions to construct uniformly-valid asymptotic solutions to autonomous and non-autonomous difference equations in the neighbourhood of a period-doubling bifurcation. In each case, we begin by constructing multiple scales approximations in which the slow time scale is treated as a continuum variable, leading to difference-differential equations. The resultant approximations fail to be asymptotic at late time, due to behaviour on the slow time scale, it is necessary to eliminate the effects of the fast time scale in order to find the late time rescaling, but there are then no difficulties with applying the method of matched asymptotic expansions. The methods that we develop lead to a general strategy for obtaining asymptotic solutions to singularly-perturbed difference equations, and we discuss clear indicators of when multiple scales, matched asymptotic expansions, or a combined approach might be appropriate.
1 citations
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TL;DR: In this paper, an asymptotic theory for a general fourth-order differential equation with large coefficients is developed. But the theory is applied with large numbers of coefficients, and the forms of the asymPTotic solutions are given under general conditions on the coefficients.
Abstract: An asymptotic theory is developed for a general fourth-order differential equation. The theory is applied with large coefficients. The forms of the asymptotic solutions are given under general conditions on the coefficients.
1 citations
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01 Dec 1976TL;DR: In this article, the uniform asymptotic stability of two types of nonautonomous linear systems is characterized in terms of the "richness" of the system elements, and the stability of these equations aries in connection with several adaptive schemes for the idenfication of the parameters of a plant with input and output measurable.
Abstract: The uniform asymptotic stability of two types of nonautonomous linear systems is characterized in terms of the "richness" of the system elements. The stability of these equations aries in connection with several adaptive schemes for the idenfication of the parameters of a plant with input and output measurable.
1 citations