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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TL;DR: In this article, the authors present a review of some results concerning delay estimation by continuous time observations of solutions of stochastic differential equations in two asymptotics: small noise limit and large samples limit.
Abstract: We present a review of some results concerning delay estimation by continuous time observations of solutions of stochastic differential equations in two asymptotics. The first one corresponds to small noise limit and the second to large samples limit. In both cases we describe the properties of the maximum likelihood estimator and Bayesian estimators with especial attention to asymptotic efficiency of the estimators. We show that the first asymptotic corresponds to regular problems of mathematical statistics and the second is close to non regular problems. In small noise asymptotics we give the next after the Gaussian term of asymptotic expansion of the maximum likelihood estimator.
8 citations
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TL;DR: In this article, a new high-frequency asymptotic theory of propagation in ducts with continuously varying refractive index is presented, based on local wave fields with complex phase and constitutes a special application of the evanescent wave tracking theory developed by the authors.
Abstract: A new high‐frequency asymptotic theory of propagation in ducts with continuously varying refractive index is presented. The theory is based on local wave fields with complex phase and constitutes a special application of the evanescent wave tracking theory developed by the authors. It is shown, for analytic profiles and for refractive indexes that vary only transversely to the duct direction, how the coefficients in the asymptotic expansion are evaluated explicitly. When the method is applied to parabolic and hyperbolic secant profiles for which exact solutions of the wave equation are available, the asymptotic expansions so generated agree term by term with the asymptotically expanded exact results. The method is then applied to a class of polynomial profiles for which exact results in terms of known functions are not available.
8 citations
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TL;DR: In this article, the authors studied the asymptotic behavior of a mutation-selection genetic algorithm on the integers with finite population of size p\ge 1, defined by the steps of a simple random walk and the fitness function is linear.
Abstract: We study the asymptotic behavior of a mutation--selection genetic algorithm on the integers with finite population of size $p\ge 1$. The mutation is defined by the steps of a simple random walk and the fitness function is linear. We prove that the normalized population satisfies an invariance principle, that a large-deviations principle holds and that the relative positions converge in law. After $n$ steps, the population is asymptotically around $\sqrt{n}$ times the position at time $1$ of a Bessel process of dimension $2p-1$.
8 citations
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TL;DR: In this paper, the Dirichlet problem in a two-dimensional domain with a narrow slit is studied, and the complete asymptotic expansion for the eigenvalue of the perturbed problem converging to a simple eigen value of the limiting problem is constructed by means of the method of matched asmptotic expansions.
Abstract: The Dirichlet problem in a two-dimensional domain with a narrow slit is studied. The width of the slit is a small parameter. The complete asymptotic expansion for the eigenvalue of the perturbed problem converging to a simple eigenvalue of the limiting problem is constructed by means of the method of matched asymptotic expansions. It is shown that the regular perturbation theory can formally be applied in a natural way up to terms of order {epsilon}{sup 2}. However, the result obtained in that way is false. The correct result can be obtained only by means of an inner asymptotic expansion.
8 citations