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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08 Feb 2002
TL;DR: In this paper, a distributional theory for asymptotic expansions of generalized functions is presented, based on a series of Dirac Delta functions, which are considered by Ramanujan and others.
Abstract: Preface * 1. Basic Results in Asymptotics * 2. Introduction to the Theory of Distributions * 3. A Distributional Theory for Asymptotic Expansions * 4. Asymptotic Expansion of Multi-Dimensional Generalized Functions * 5. Asymptotic Expansion of Certain Series Considered by Ramanujan * 6. Cesaro Behavior of Distributions * 7. Series of Dirac Delta Functions * References * Index
98 citations
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97 citations
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TL;DR: In this paper, the upper and lower limits of an arithmetic function for large values of its argument have been investigated, and the first result in this line was obtained by LANDAU:t.
Abstract: While formerly the research of asymptotic expressions in the theory of numbers was largely confined to the approximate determination of the summatory function (or the mean value) of a given arithmetic function, recent progress in the theory of prime numbers has opened a new field for asymptotic investigations, viz., the research of upper and lower limits of an arithmetic function for large values of its argument. The first result in this line was obtained by LANDAU:t
97 citations
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01 Jan 1993
TL;DR: This paper presents a meta-modelling of Complex Systems with Asymptotic-Enhanced Numerical Methods and its applications in Scientific Computing and Symbolic Manipulation Tools for AsymPTotic Analysis.
Abstract: Preface. Part 1: Modeling of Complex Systems with Asymptotic-Enhanced Numerical Methods. Part 2: Asymptotic-Induced Domain Decomposition Methods. Part 3: Multiple-Scale Problems in Scientific Computing. Part 4: Applied and Asymptotic Analysis. Part 5: Symbolic Manipulation Tools for Asymptotic Analysis. Part 6: Numerical Methods, Algorithms, and Architectures. Index.
97 citations
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TL;DR: In this paper, the authors studied the asymptotic theory of Bayes solutions in estimating and testing when hypothesis and alternative are separated at least by an indifference region, under the assumption that the observations are independent and indentically distributed.
Abstract: This paper deals with the asymptotic theory of Bayes solutions in (i) Estimation (ii) Testing when hypothesis and alternative are separated at least by an indifference region, under the assumption that the observations are independent and indentically distributed. The estimation results which are partial generalizations of results of LeCam begin with a proof of the convergence of the normalized posterior density to the appropriate normal density in a strong sense. From this result we derive the asymptotic efficiency of Bayes estimates obtained from smooth loss functions and in particular of the posterior mean. The last two theorems of this section deal with asymptotic expansions for the posterior risk in such estimation problems. The section on testing contains a limit theorem for the n-th root of the posterior risk under weak conditions on the prior and the loss function. Finally we discuss generalizations and some open problems.
95 citations