Showing papers on "Asymptotology published in 1991"

Asymptotic analysis of stochastic programs

Abstract: In this paper we discuss a general approach to studying asymptotic properties of statistical estimators in stochastic programming. The approach is based on an extended delta method and appears to be particularly suitable for deriving asymptotics of the optimal value of stochastic programs. Asymptotic analysis of the optimal value will be presented in detail. Asymptotic properties of the corresponding optimal solutions are briefly discussed.

An asymptotic analysis of the one-dimensional Vlasov-Poisson system : the Child-Langmuir law

Abstract: 187 Degond, P. and P.A. Raviart, An asymptotic analysis of the one-dimensional Vlasov-Poisson system: the Child-Langmuir law, Asymptotic Analysis 4 (1991) 187-214. We perform the asymptotic analysis of the one-dimensional Vlasov-Poisson system when singular boundary data are prescribed. Such a singular perturbation problem arises in the modelling of vacuum diodes under very large applied bias, and gives rise to the well-known "Child-Langmuir law". In this paper, we provide a mathematical framework to this physical theory, by successively investigating the reduced problem (when the perturbation parameter e is set equal to zero) and the boundary layer problem, which gives a sharp qualitative information.

Asymptotic theory of sequential estimation : Differential geometrical approach

Abstract: Sequential estimation continues observations until the observed sample satisfies a prescribed criterion. Its properties are superior on the average to those of nonsequential estimation in which the number of observations is fixed a priori. A higher-order asymptotic theory of sequential estimation is given in the framework of geometry of multidimensional curved exponential families. This gives a design principle of the second-order efficient sequential estimation procedure. It is also shown that a sequential estimation can be designed to have a covariance stabilizing effect at the same time.

Higher order asymptotic theory for time series analysis

Abstract: A survey of the first-order asymptotic theory for time series analysis higher order asymptotic theory for gussian arma processes validity of Edgeworth expansions in time series analysis higher order asymptotic sufficiency, asymptotic ancillarity in time series analysis higher order investigations for testing theory in time series analysis higher order asymptotic theory for multivariate time series some practical examples.

Refined engineering beam theory based on the asymptotic expansion approach

Abstract: A systematic derivation of a refined engineering theory governing the response of elastic beams is presented. The method employed to accomplish this is that of asymptotic expansion that combines dimensional analysis with the expansion in powers of a small parameter of the solution of the three-dimensional linear elasticity theory. The present beam theory contains more information than the classical Timoshenko theory. A new shear coefficient is defined and compared with existing ones.

Saddle Point Techniques in Asymptotic Coding Theory

Abstract: We use asymptotic estimates on coefficients of generating functions to derive anew the asymptotic behaviour of the volume of Hamming spheres and Lee spheres for small alphabets We then derive the asymptotic volume of Lee spheres for large alphabets, and an asymptotic relation between the covering radius and the dual distance of binary codes

On the third quantization of general relativity

Abstract: The author studies the possibility of defining a Hilbert space for n=(d+1)-dimensional general relativity in some asymptotic regions of Wheeler's superspace. The author distinguishes two asymptotic regions: (i) the 'classical asymptotic region', which contains geometries with a volume much larger than the Planck volume and (ii) the 'quantum asymptotic region', which contains geometries with a volume much smaller than the Planck volume. It is shown that for n>or=4 one can define a Hilbert space only in the classical asymptotic region of superspace, while for n(4 one can define a Hilbert space in the quantum asymptotic region or in the classical asymptotic region, but not both. It is argued that in a good theory of quantum gravity one should be able to define a Hilbert space in the two asymptotic regions. Therefore it seems that Einstein's general relativity is not a good candidate for a quantum theory of gravitation. But it (the 3+1)-dimensional case) can be a good classical limit of that theory. The above criterion can serve in the search for a quantum theory of gravitation.

Asymptotic analysis of singularly perturbed systems of ordinary differential equations

Abstract: Atmtract--Pre~mt ed in this paper is a new algorithm for the asymptotic expansion of a solution to an initial value problem for ~ngularly perturbed (stiff) systems of ordinary dlfferemtial eqtmtlons. This algorithm is related to the Chapman-Enskog asymptotic expamdon method mind in the kinetic theory to derive the equatiorm of hydrodynamics, whcxeas the standard algorithm pertains to the Hilbert approach known to give inferior results. In cases of systems of ordinary differential equatioms the new algorithm leads to the reduction of numerical effort needed to achieve a given accuracy M compm-ed with the st~mdard uymptotlc expansion method. The proof of the asymptotic c~vc=lpmce is given. The numerical example demonstrates the feasibility of the new approach.

Asymptotic solution of a variational inequality modeling friction

Abstract: The problem of minimizing the nondifferentiable functional is considered. An asymptotic solution of the corresponding variational inequality is constructed and justified under the assumption that or is a small parameter. Also, formal asymptotic representations are obtained for singular surfaces which characterize a change in the type of boundary conditions. For a modification of the Vishik-Lyusternik method is used, and exponential boundary layers arise. If , then the boundary layer has only power growth; the principal term of the asymptotic expansion of the solution of the problem in a multidimensional region and the complete asymptotic expansion for the case are obtained.

On the asymptotic behavior of the coefficients of asymptotic power series and its relevance to stokes phenomena

Abstract: This paper discusses the relevance of the asymptotic behavior of the coefficients of asymptotic power series for the study of Stokes phenomena By way of illustration a connection problem is considered in the theory of linear difference equations

Hamiltonian formulation for Kaluza-Klein spaces asymptotic to the KKM solution

Abstract: The author gives a complete description of the phase space in the Kaluza-Klein theory with asymptotic behaviour inspired from that of the Kaluza-Klein monopole solution. This is done by exhibiting the explicit asymptotic and parity conditions that the metrics and momenta must satisfy. This allows one to give the definitions of the Hamiltonian, the linear and angular momenta, the generators of asymptotic boosts and the electrical charge.

Asymptotic analysis of almost periodic weakly non-linear systems

Abstract: Asymptotic solutions of weakly non-linear oscillatory systems are considered in this paper. An algorithm is given for constructing an Nth order asymptotic solution for a class of such systems. The asymptotic solution is almost periodic and has a two-time scale property. Fourier like projections are introduced and used in this paper together with perturbation techniques to arrive at the sought asymptotic solution. The results in this paper extend the results by Hoogstraten and Kaper (1975).