Showing papers on "Asymptotology published in 1992"
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153 citations
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89 citations
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TL;DR: Positive recurrent potential theory is reviewed, giving special attention to continuous-time Markov chains, and explicit formulas for birth-and-death processes and diffusion processes, and recursive computational procedures for skip-free chains are provided.
Abstract: The simulation run length required to achieve desired statistical precision for a sample mean in a steady-state stochastic simulation experiment is largely determined by the asymptotic variance of the sample mean and, to a lesser extent, by the second-order asymptotics of the variance and the asymptotic bias. The asymptotic variance, the second-order asymptotics of the variance, and the asymptotic bias of the sample mean of a function of an ergodic Markov process can be expressed in terms of solutions of Poisson's equation, as indicated by positive recurrent potential theory. We review this positive recurrent potential theory, giving special attention to continuous-time Markov chains. We provide explicit formulas for birth-and-death processes and diffusion processes, and recursive computational procedures for skip-free chains. These results can be used to help design simulation experiments after approximating the stochastic process of interest by one of the elementary Markov processes considered here.
66 citations
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TL;DR: In this article, an asymptotic behavior of any possible solution of the second Painleve equation near infinity is described, and connection formulas for the parameters of the asymPTotic description are presented as well.
66 citations
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58 citations
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TL;DR: An efficient closed-form asymptotic representation for the grounded double-layer (substrate-superstrate) Green's function is presented in this paper, which is valid for both source (a horizontal electric dipole) and observation points anywhere inside the superstate or at interfaces.
Abstract: An efficient closed-form asymptotic representation for the grounded double-layer (substrate-superstrate) Green's function is presented. The formulation is valid for both source (a horizontal electric dipole) and observation points anywhere inside the superstate or at the interfaces. The asymptotic expressions are developed via a steepest descent evaluation of the original Sommerfeld-type integral representation of the Green's function, and the large parameter in this asymptotic development is proportional to the lateral separation between source and observation points. The asymptotic solution is shown to agree with the exact Green's function for lateral distances even as small as a few tenths of the free-space wavelengths, thus constituting a very efficient tool for analyzing printed circuits/antennas. Since the asymptotic approximation gives separate contributions pertaining to the different wave phenomena, it provides physical insight into the field behavior, as shown by examples. >
38 citations
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TL;DR: In this paper, the distribution function of the first few terms in a stochastic expansion of an econometric estimator or test statistic provided an asymptotic approximation to the original estimator with an error of order less than that of the limiting normal or chi-square approximation.
Abstract: Under general conditions the distribution function of the first few terms in a stochastic expansion of an econometric estimator or test statistic provides an asymptotic approximation to the distribution function of the original estimator or test statistic with an error of order less than that of the limiting normal or chi-square approximation. This can be used to establish the validity of several refined asymptotic methods, including the comparison of Nagar-type moments and the use of formal Edgeworth or Edgeworth-type approximations.
38 citations
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26 citations
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TL;DR: The Euler-Poincare equations describing geodesics on Lie groups with invariant metrics fall into the class of quasihomogeneous systems with homogeneous quadratic right-hand members as mentioned in this paper.
Abstract: An example is a system with homogeneous quadratic right-hand members: in it, gl = ... = gn = i. Among others, the Euler-Poincare equations describing geodesics on Lie groups with invariant metrics fall into this class. A popular example from dynamics is Kirchoff's problem on the motion of a rigid body in an unbounded volume of an ideal liquid. Quasihomogeneous systems are also exemplified by the equations of the problem of many gravitating bodies and by the Euler-Poisson equations describing the rotation of a heavy rigid body about a fixed point. These remarks show that it is expedient to consider quasihomogeneous systems from the viewpoint of applications.
19 citations
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TL;DR: In this paper, a systematic study of the Robinson-Trautman metrics in the asymptotic future is presented, and a technique that could be used for determining existence of solutions of the RTA equation is found.
Abstract: A systematic study of the Robinson-Trautman metrics in the asymptotic future is presented. As a by-product another technique, that could be used for determining existence of solutions of the Robinson-Trautman equation, is found. All these metrics present an exponential asymptotic limit to the Schwarzschild metric in this regime.
16 citations
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01 Aug 1992
TL;DR: Based on previous work on asymptotic expansions, this work gives an algorithm which computes Hardy-field solutions of equations f(y) = x, with f belonging to a large class of functions.
Abstract: We study the automatic computation of asymptotic expansions of functional inverses. Based on previous work on asymptotic expansions, we give an algorithm which computes Hardy-field solutions of equations f(y) = x, with f belonging to a large class of functions.
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TL;DR: In this paper, the stability properties of the error dynamics are studied in the original coordinates and it is shown how the asymptotic stability in the new coordinates does not imply, in general, the original ones.
Abstract: Observer design for non-linear systems is discussed. Some recent approaches are based on state and output change of coordinates to transform a non-linear system into a particular observer form, from which an asymptotic observer can be designed ensuring the asymptotic stability of the error dynamics in the new coordinates. In this paper, the stability properties of the error dynamics are studied in the original coordinates. With some examples, it is shown how the asymptotic stability in the new coordinates does not imply, in general, the asymptotic stability in the original ones. Some general results are stated and proved to guarantee the asymptotic stability of the error dynamics in the original coordinates.
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TL;DR: The equichordal problem was first raised by Klee as discussed by the authors, who pointed out that the existence of a simple closed curve with two equichoral points is very unlikely, but no proof demonstrating the nonexistence has yet been given.
Abstract: The equichordal problem asks whether there exists an equichordal curve, i.e. a simple closed curve in the plane with two equichordal points. An equichordalpoint of a simple closed curve is a point such that every line passing through the point meets the curve in exactly two points and all chords determined in this way have the same length. According to Klee [5] the problem was first raised by Fujiwara [4] in 1916 and independently by Blaschke, Rothe and Weitzenb ck [1] in 1917. The problem has been investigated by S ss [10], Dirac [2], Wirsing [11], Ehrhart [3] and others. Several of these authors pointed out that the existence of an equichordal curve is very unlikely but no proof demonstrating the nonexistence has been given so far.
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TL;DR: In this paper, the authors apply regularization of divergent integrals in the derivation of the asymptotic expansion of certain multi-dimensional generalized functions, which provides a lucid formulation of the expansion of oscillatory integrals.
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TL;DR: A new asymptotic scheme for intensity statistics of waves in random media with a pure power-law correlation is presented and provides effective and accurate asymPTotic expansion series for all intensity moments.
Abstract: A new asymptotic scheme for intensity statistics of waves in random media with a pure power-law correlation is presented. In the strong scattering regime it provides effective and accurate asymptotic expansion series for all intensity moments. The new first-order result, which is considerably more accurate than that from the existing asymptotic theory, may also serve as a starting point for useful statistical models.
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01 Jan 1992
TL;DR: This thesis focuses on the single link method and a detailed general framework is developed to deal with hierarchical structure in either the sample or the population case, establishing the equivalence of hierarchies and ultrametric distances, define single-link distances and derive the connection to minimal spanning trees.
Abstract: The main theme of this thesis is the study of the asymptotic and computational aspects of clustering analysis for samples of iid observations in an effort to improve upon the older methods. We are concerned with hierarchical clustering methods and we focus on the single link method. First, a detailed general framework is developed to deal with hierarchical structure in either the sample or the population case. In this general setting, we establish the equivalence of hierarchies and ultrametric distances, define single-link distances and derive the connection to minimal spanning trees. The next step is to study the behavior of single-link distances between iid observations drawn from probability distributions whose support is compact and has a finite number of connected components. For such distributions, we prove the consistency of single-link distances and in the case of one dimensional distributions we obtain an asymptotically normal distribution for the average single link distance using facts about spacings. In the case of multivariate distributions and under some conditions, we obtain the rate of convergence for the maximum single-link distance (which is equal to the length of the longest edge of the minimal spanning tree) and give upper and lower bounds. To deal with the chaining problem in real data, we combine kernel density estimation with the computation of minimal spanning trees to study the effect of density truncation on single-link partitions. New statistics are proposed to help decide on the best truncation level, leading to an improved version of the single-link method. Simulation studies show how these statistics perform with un:modal and bimodal densities. Finally, these tools are applied to two cluster,... xam-ples: One involves grouping several foods according to the nutrients they contain. The other is a market segmentation study, concerning an Atlanta manufacturer of prefabricated homes. ToUr' aCirb roizvvy v iC 6 7rp66Owv A6yo dKrairL , ro !ar 'iv / v a i iroAAcd acbrcv I?/Kdrpov, Ktai mrD1 l • k • 'tpa ci0), dAA& rT& irore dpLO/6v kdrepov lp7rpooOcv CitrirmaL Trof) 6irELp ai'rwv 'EKarac 770ovLivaL; This is exactly what the previous discussion requires from us: How is it possible for each of them to be one and many at the same time and how is it they do not immediately become Infinity but instead they first acquire a finite number before each of them becomes Infinity? Plato, Philebus 19A. To my family, for their love and support. Acknowledgements New ideas …
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TL;DR: Asymptotic properties of a nonlinear two-dimensional system of differential equations were studied using the topological method of Wazewski in this paper, and the results showed that the system can be represented as a convex polygon.
Abstract: Asymptotic properties of a nonlinear two-dimensional system of differential equations are studied using the topological method of Wazewski.
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TL;DR: In this article, the three-dimensional dynamical equations of the theory of elasticity for the bending of a plate are subjected to asymptotic analysis and two dimensionless parameters (the exponents of variability and dynamism) characterizing the stress-strain state (SSS) of the plate are varied independently.
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01 Jan 1992
TL;DR: In this article, a two-level system of boundary integral equations is derived and analyzed for the three structural-acoustic coupling problems, and some numerical results based on asymptotic analysis are presented.
Abstract: A two-level system of boundary integral equations are derived and analyzed for the three structural-acoustic coupling problems. The advanced formulation of boundary integral equations method, suggested by Slepyan and Sorokin [1,2] is used. Some numerical results based on asymptotic analysis are presented.
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01 Jan 1992
TL;DR: In this paper, the asymptotic behavior of solutions to nonlinear evolution equations associated to monotone operators is investigated from the same point of view as in this paper.
Abstract: In this paper we deal with the asymptotic behaviour of solutions to some nonlinear evolution equations associated to monotone operators. Some first order difference equations are also investigated from the same point of view.
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01 Jan 1992TL;DR: In this article, a sketch of a geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through short-range pair potentials is given.
Abstract: We give a sketch of a geometrical proof of asymptotic completeness for an arbitrary number of quantum particles interacting through short-range pair potentials.