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Showing papers on "Asymptotology published in 2010"




Journal ArticleDOI
TL;DR: A loss of asymptotic order is observed, but in the most relevant cases the overall asymaptotic order remains higher than a truncated asymPTotic expansion at similar computational effort.
Abstract: We propose a variant of the numerical method of steepest descent for oscillatory integrals by using a low-cost explicit polynomial approximation of the paths of steepest descent. A loss of asymptotic order is observed, but in the most relevant cases the overall asymptotic order remains higher than a truncated asymptotic expansion at similar computational effort. Theoretical results based on number theory underpinning the mechanisms behind this effect are presented.

38 citations



Journal ArticleDOI
TL;DR: In this article, a general asymptotic theory for the estimation of strictly stationary and ergodic time series models is developed, under simple conditions that are straightforward to check.
Abstract: This paper develops a general asymptotic theory for the estimation of strictly stationary and ergodic time–series models. Under simple conditions that are straightforward to check, we establish the strong consistency, the rate of strong convergence and the asymptotic normality of a general class of estimators that includes LSE, MLE and some M-type estimators. As an application, we verify the assumptions for the long-memory fractional ARIMA model. Other examples include the GARCH(1,1) model, random coefficient AR(1) model and the threshold MA(1) model.

30 citations


Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotic behavior of solutions of a mixed inhomogeneous boundary value problem and a spectral Neumann problem in a thin perforated domain with rapidly varying thickness.
Abstract: For a second-order symmetric uniformly elliptic differential operator with rapidly oscillating coefficients, we study the asymptotic behavior of solutions of a mixed inhomogeneous boundary-value problem and a spectral Neumann problem in a thin perforated domain with rapidly varying thickness. We obtain asymptotic estimates for the differences between solutions of the original problems and the corresponding homogenized problems. These results were announced in Dopovidi Akademii Nauk Ukrainy, No. 10, 15‐19 (1991). The new results obtained in the present paper are related to the construction of an asymptotic expansion of a solution of a mixed homogeneous boundary-value problem under additional assumptions of symmetry for the coefficients of the operator and for the thin perforated domain.

28 citations


Journal ArticleDOI
TL;DR: This paper considers estimates of law-invariant or version-independent coherent risk or acceptability functionals based on the empirical distribution function and investigates their asymptotic properties.
Abstract: Law-invariant or version-independent coherent risk or acceptability functionals do not explicitly depend on the underlying probability space and can be considered as functionals of the distribution function. In this paper, we consider estimates of these functionals based on the empirical distribution function and investigate their asymptotic properties.

26 citations


Posted Content
TL;DR: In this article, the authors derive new simple explicit formulas for the coefficients of the asymptotic expansion to the sequence of factorials, using a theorem of Howard for a formula recently proved by Brassesco and M\'endez.
Abstract: Applying a theorem of Howard for a formula recently proved by Brassesco and M\'endez, we derive new simple explicit formulas for the coefficients of the asymptotic expansion to the sequence of factorials. To our knowledge no explicit formula containing only the four basic operations was known until now.

25 citations


Journal ArticleDOI
TL;DR: In this paper, a method is presented for modeling bonding processes and interfaces on thin layers, where the contact and pseudo-friction conditions between the adhesive and the adherents are also taken into account.

25 citations


Journal ArticleDOI
TL;DR: The aim of this paper is to construct some asymptotic expansions which produce increasingly accurate approximations of the gamma function.
Abstract: The aim of this paper is to construct some asymptotic expansions which produce increasingly accurate approximations of the gamma function.

21 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated the nonhomogeneous initial boundary value problem for the Camassa-Holm equation on an interval, and established a result on the global asymptotic stabilization problem by means of a boundary feedback law.

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the relation between the moments and the asymptotic behavior of solutions to the Burgers equation and showed that the convergence order increases by a similarity scale whenever the order of controlled moments is increased by one.

Journal ArticleDOI
TL;DR: In this paper, the asymptotic behavior of recursive estimation procedures is studied and the results of the analysis can be used to determine the form of the recursive procedure which is expected to have the same properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation.
Abstract: This paper is concerned with the asymptotic behaviour of estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The results of the paper can be used to determine the form of the recursive procedure which is expected to have the same asymptotic properties as the corresponding non-recursive one defined as a solution of the corresponding estimating equation. Several examples are given to illustrate the theory, including an application to estimation of parameters in exponential families of Markov processes.

Journal ArticleDOI
TL;DR: In this paper, the authors prove results on the asymptotic behavior of scalar perturbations both in the approach to the initial singularity of the background model and at late times.
Abstract: In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein–Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behavior of scalar perturbations both in the approach to the initial singularity of the background model and at late times. The main equation of interest is a linear hyperbolic equation whose coefficients depend only on time. Expansions for the solutions are obtained in both asymptotic regimes. In both cases, it is shown how general solutions with a linear equation of state can be parametrized by certain functions which are coefficients in the asymptotic expansion. For some nonlinear equations of state, it is found that the late-time asymptotic behavior is qualitatively different from that in the linear case.

Journal ArticleDOI
TL;DR: In this article, the authors derive and justify two models for bending-stretching of a viscoelastic rod by using the asymptotic expansion method, and derive a model for bending and stretching of the rod.

Journal ArticleDOI
TL;DR: In this article, the global asymptotic stability of the equilibrium point for the fractional difference equation was studied and the stability was shown to be robust to perturbations.
Abstract: We study the global asymptotic stability of the equilibrium point for the fractional difference equation 𝑥𝑛


Journal ArticleDOI
TL;DR: In this paper, the authors consider a class of non-autonomous, degenerate parabolic equations and study the asymptotic behavior of the solutions. But their results are restricted to the case where the solution depends explicitly upon the time of the equation.
Abstract: We consider a class of non-autonomous, degenerate parabolic equations and we study the asymptotic behaviour of the solutions. Even if the equation depends explicitly upon the time, we prove that several asymptotic properties, valid for the autonomous case, are preserved in this more general situation. To our knowledge, it is the first time that the asymptotic behaviour of solutions to non-autonomous equations is studied.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: In this article, the asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied, and the authors investigated the non-stationary K-functions for a class of nonstationary processes, where stationary is often not a reasonable assumption.
Abstract: The K-function is one of the most commonly used summary statistics. It plays the role for spatial point processes that the covariance function or the variogram plays for continuous observation. The asymptotic properties of the nonparametric estimation of K-function in stationary spatial point processes have been studied. However, in practice, stationary is often not a reasonable assumption. In this article, we investigate the asymptotic behaviour of the nonparametric estimation of K-function for a class of nonstationary processes.

Journal Article
TL;DR: In this paper, the authors developed an approach based on state asymptotic estimator for distributed diffusion F-systems, where the dynamical systems are uncontrolled (Fsystems).
Abstract: The aim of this paper is to develop an approach based on state asymptotic estimator. More precisely, we extend the notion of regional asymptotic observability as in ref. [1] to the case where the dynamical systems are uncontrolled (Fsystems). For different sensors, we give the characterizations of regional asymptotic free observer in order that asymptotic free observability can be achieved. Furthermore, we show that, there exists a dynamical F-system for distributed diffusion F-system is not asymptotic F-observable in the usual sense, but it may be regional asymptotic Fobservable.

Journal ArticleDOI
TL;DR: A uniform asymptotic expansion for the integral ∫∫s▽2udxdy, where u is the solution of the Neumann problem with a delta-function-like derivative on the boundary, was found in this article.
Abstract: A uniform asymptotic expansion is found for the integral ∫∫s▽2udxdy, where u is the solution of the Neumann problem with a delta-function-like derivative on the boundary. A physics application of the result is discussed.

Journal ArticleDOI
TL;DR: In this article, the authors introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales, which is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid expansion.
Abstract: In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases.

Journal Article
TL;DR: In this article, the boundary value problem of a class of singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters is considered.
Abstract: The boundary value problem of a class of singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters is considered.Under some suitable conditions,a formal asymptotic expansion of the solution is constructed.By using the fixed theorem,the existence and asymptotic behavior of the solution are studied.

Journal ArticleDOI
TL;DR: It is shown that the regular perturbation theory can formally be applied in a natural way up to terms of order e2 and the eigenvalue of the perturbed problem can be both more and less than the eigens of the limiting problem subject to the position and geometry of the slit.
Abstract: The Neumann problem in two-dimensional domain with a narrow slit is studied. The width of the slit is a small para- meter 0

Journal ArticleDOI
TL;DR: In this paper, a uniform asymptotic approximation to the solution up to an arbitrary power of the small parameter is constructed and substantiated, where the solution has quite a complicated structure.
Abstract: The initial value problem for a system of nonlinear ordinary differential equations with a small parameter multiplying the highest derivative is investigated. In a neighbourhood of the initial point the asymptotic behaviour of the solution has quite a complicated structure. A uniform asymptotic approximation to the solution up to an arbitrary power of the small parameter is constructed and substantiated. Bibliography: 3 titles.

Journal ArticleDOI
TL;DR: In this article, the authors studied the asymptotics of first-order nonlinear difference equations and provided sufficient conditions for the existence of an actual solution with such as-ymptotic behaviour.
Abstract: ¯We study the asymptotics of first-order nonlinear difference equations. In particular we present an asymptotic functional equation for potential asymptotic behaviour, and a theorem stating sufficient conditions for the existence of an actual solution with such asymptotic behaviour.

Book ChapterDOI
01 Jan 2010
TL;DR: In this paper, the authors studied the borrower's optimal strategy to close the mortgage when the volatility of the market investment return is small and derived asymptotic expansions of the free boundary for both small time and large time.
Abstract: This paper studies the borrower’s optimal strategy to close the mortgage when the volatility of the market investment return is small. Integral equation representation of the mortgage contract value is derived, then used to find the numerical solution of the free boundary. The asymptotic expansions of the free boundary are derived for both small time and large time. Based on these asymptotic expansions two simple analytical approximation formulas are proposed. Numerical experiments show that the approximation formulas are accurate enough from practitioner’s point of view.

Journal ArticleDOI
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.

Journal ArticleDOI
TL;DR: A complete asymptotic expansion for a sequence of certain sums is derived that solves a problem recently proposed in the Research Group in Mathematical Inequalities and Applications (RGMIA) mailing list.