scispace - formally typeset
Search or ask a question
Topic

Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, the authors considered the problem of determining logarithmic, as well as polynomial, asymptotic estimates for certain convergent integrals containing parameters.
Abstract: In this paper, we consider the problem of determining logarithmic, as well as polynomial, asymptotic estimates for certain convergent integrals containing parameters. We state and prove an asymptotic theorem which gives the logarithmic asymptotic behavior of a convergent integral where any subset of the parameters becomes large while the remaining parameters remain bounded. This theorem is then applied to the photon and electron self‐energy graphs of quantum electrodynamics.

39 citations

Journal ArticleDOI
TL;DR: This book is strongly recommended for those interested in the use of asymptotics in statistics and probability problems, and provides a quick and accessible overview of the available results, providing both a basic understanding of their context and references to sources where a more detailed treatment can be found.
Abstract: Asymptotic Theory of Statistics and Probability, by Anirban DasGupta, New York, Springer, 2008, xxvii+722 pp., £55.99 or US$89.95 (hardback), ISBN 978-0-387-75970-8 Unlike many books on asymptotic ...

39 citations

Journal ArticleDOI
TL;DR: It is shown that using values of the integrand at certain complex points close to the critical points can actually yield a higher asymptotic order approximation to the integral.
Abstract: Asymptotic expansions for oscillatory integrals typically depend on the values and derivatives of the integrand at a small number of critical points. We show that using values of the integrand at certain complex points close to the critical points can actually yield a higher asymptotic order approximation to the integral. This superinterpolation property has interesting ramifications for numerical methods based on exploiting asymptotic behaviour. The asymptotic convergence rates of Filon-type methods can be doubled at no additional cost. Numerical steepest descent methods already exhibit this high asymptotic order, but their analyticity requirements can be significantly relaxed. The method can be applied to general oscillators with stationary points as well, through a simple change of variables.

39 citations

Journal ArticleDOI
TL;DR: In this paper, the asymptotic properties of least squares estimates of Hammerstein-Wiener model structures are investigated, and a consistent procedure for the estimation of the variance of the parameter estimates is provided.
Abstract: This paper investigates the asymptotic properties of least squares estimates of Hammerstein-Wiener model structures, and in doing so establishes consistency and asymptotic normality under fairly mild conditions on the additive noise process, the inputs and the static non-linearities. In relation to the asymptotic distributional results, a consistent procedure for the estimation of the asymptotic variance of the parameter estimates is provided. A key theme of this paper is to demonstrate how recent results from the econometrics literature may be employed in an engineering setting. In this respect the Hammerstein-Wiener model structure serves as a demonstration example. A simulation study complements the theoretical findings.

38 citations

Journal ArticleDOI
TL;DR: In this article, the harmonic potential of a random walk has been shown to have arbitrary precision asymptotics, and two algorithms that allow to obtain arbitrary precision harmonic potentials for random walks are given.
Abstract: We give two algorithms that allow to get arbitrary precision asymptotics for the harmonic potential of a random walk.

38 citations


Network Information
Related Topics (5)
Stochastic partial differential equation
21.1K papers, 707.2K citations
84% related
Differential equation
88K papers, 2M citations
83% related
Numerical partial differential equations
20.1K papers, 703.7K citations
82% related
Bounded function
77.2K papers, 1.3M citations
81% related
Partial differential equation
70.8K papers, 1.6M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526