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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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Journal ArticleDOI
TL;DR: This note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems (SDSs) where the systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition.
Abstract: This note is concerned with the asymptotic stability analysis for nonlinear stochastic differential systems (SDSs). The systems coefficients are assumed to satisfy local Lipschitz condition and polynomial growth condition. By applying some novel techniques, some easily verifiable conditions are obtained which ensure the almost sure asymptotic stability and pth moment asymptotic stability for such SDSs. We also provide the range of the order p. A numerical example is provided to illustrate the effectiveness and the benefits of the proposed result.

32 citations

Proceedings ArticleDOI
10 Dec 2002
TL;DR: In this article, the convergence to the asymptotic results is so fat that even for moderate parameter values they yield results close to the true values, and the authors illustrate this principle through a number of examples taken from multiple-antenna systems.
Abstract: Asymptotic theorems are very commonly used in probability. For systems whose performance depends on a set of random variables, asymptotic analyses are often used to simplify calculations and obtain results yielding useful hints at the behavior of the system when the parameters take on finite values. These asymptotic analyses are especially useful whenever the convergence to the asymptotic results is so fat that even for moderate parameter values they yield results close to the true values. The goal of this paper is to illustrate this principle through a number of examples taken from multiple-antenna systems.

32 citations

Journal ArticleDOI
TL;DR: In this article, a complete asymptotic expansion for eigenvalues of the Lame system of the linear elasticity in domains with small inclusions in three dimensions was derived by an integral equation formulation of the solutions to the harmonic oscillatory linear elastic equation.
Abstract: We derive a complete asymptotic expansion for eigenvalues of the Lame system of the linear elasticity in domains with small inclusions in three dimensions. By an integral equation formulation of the solutions to the harmonic oscillatory linear elastic equation, we reduce this problem to the study of the characteristic values of integral operators in the complex planes. Generalized Rouche's theorem and other techniques from the theory of meromorphic operator-valued functions are combined with asymptotic analysis of integral kernels to obtain full asymptotic expansions for eigenvalues.

32 citations


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