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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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2 citations
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TL;DR: In this paper, the distribution of the time to emptiness of a finite dam or reservoir might be investigated by the use of Wald's identity, which has recently been used by R. M. Phatarfod2 in the case of inputs with negative exponential distribution and is useful as an approximation in all cases where individual (independent) increments are fairly small in relation to the capacity of the dam.
Abstract: IN my contribution to the discussion at a symposium1 in 1957 on the theory of dams, I suggested that the distribution of the time to emptiness of a finite dam or reservoir might be investigated by the use of Wald's identity. This method has recently been used by R. M. Phatarfod2 in the case of inputs with negative exponential distribution. It seems worth noting how the asymptotic case of normal diffusion, which should be useful as an approximation in all cases where individual (independent) increments are fairly small in relation to the capacity of the dam, may be dealt with. This asymptotic theory has, moreover, an immediate extension to the case of correlated increments by our determining the effective diffusion per unit time in such a case (compare with my concluding remarks, loc. cit.).
2 citations
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01 Jan 1971
2 citations
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TL;DR: In this article, the authors investigated the asymptotic equilibrium of the integro-differential equations with infinite delay in a Hilbert space and showed that the problem is NP-hard.
Abstract: The asymptotic equilibrium problems of ordinary differential equations in a Banach space have been considered by several authors. In this paper, we investigate the asymptotic equilibrium of the integro-differential equations with infinite delay in a Hilbert space.
2 citations
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TL;DR: In this article, the authors study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with a rapidly oscillating boundary.
Abstract: We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with a rapidly oscillating boundary. We consider both cases where the eigenvalues of the limit problem are simple and multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics.
2 citations