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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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TL;DR: In this article, general results concerning the asymptotic behavior of the Polyak averaging of the solution of the Robbins-Monro type stochastic differential equation are presented.
Abstract: General results concerning the asymptotic behaviour of the Polyak averaging of the solution of the Robbins-Monro type stochastic differential equation are presented. It is shown that the suitable normalized process admits an asymptotic expansion which enables one to obtain its asymptotic distribution from a central limit theorem for martingales.

7 citations

Journal ArticleDOI
TL;DR: The asymptotic results obtained in this paper admit generalizations for an isotropic medium with arbitrary S matrix, and they can be reduced to simple replacements of the scalar by vector relations.
Abstract: The asymptotic results obtained above admit generalizations. First, one can take into account polarization. For an isotropic medium with arbitrary S matrix, allowance for polarization in the framework of the asymptotic theory developed here reduces in fact to simple replacements of the scalar by vector relations. Second, at least some of the results must remain true for a large class of inhomogeneous media. This is because angular relaxation also occurs in inhomogeneous media, and there must be asymptotic separation of the variables.

7 citations

Journal ArticleDOI
TL;DR: In this paper, a proof of their main asymptotic results is given, which depends on substantially weakened hypotheses and is based on the mathematical basis of their method of inequalities.
Abstract: Ho & Meyer [1] have sketched an argument for arriving at asymptotic properties of solutions of a pair of non-linear conservation laws with floating, shocktype boundary condition of importance in gas dynamics and oceanography. To clarify the mathematical basis of their method of inequalities, a proof of their main asymptotic results is given here. It depends on substantially weakened hypotheses.

7 citations


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