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171.
Guowu Yao 《Proceedings of the American Mathematical Society》2004,132(8):2483-2493
Let be a sequence of locally quasiconformal harmonic maps on the unit disk with respect to the Poincaré metric. Suppose that the energy densities of are uniformly bounded from below by a positive constant and locally uniformly bounded from above. Then there is a subsequence of that locally uniformly converges on , and the limit function is either a locally quasiconformal harmonic map of the Poincaré disk or a constant. Especially, if the limit function is not a constant, the subsequence can be chosen to satisfy some stronger conditions. As an application, it is proved that every point of the space , a subspace of the universal Teichmüller space, can be represented by a quasiconformal harmonic map that is an asymptotic hyperbolic isometry.
172.
We derive asymptotic expansions for tails of infinite weighted convolutions of some heavy-tailed distributions. Applications
are given to tail expansion of the marginal distribution of ARMA processes, randomly stopped sums, as well as limiting waiting
time distribution.
AMS 2000 Subject Classifications. Primary—62E99, Secondary—41A60, 44A35, 60G50, 60K25 相似文献
173.
Buldygin Valery Utzet Frederic Zaiats Vladimir 《Statistical Inference for Stochastic Processes》2004,7(1):1-34
The problem of estimation of an unknown response function of a time-invariant continuous linear system is considered. Discrete-time sample input–output cross-correlograms are taken as estimates of the response function. The inputs are supposed to be zero-mean stationary Gaussian processes close, in some sense, to a white noise. Both asymptotic normality of finite-dimensional distributions of the estimates and their asymptotic normality in spaces of continuous functions are studied. Our basic tool is a new integral representation for cumulants of the estimate as a finite sum of integrals involving cyclic products of kernels. Some inequalities for these integrals are obtained and their asymptotic behaviour is studied. 相似文献
174.
In this paper strongly nonlinear oscillator equations will be studied.It will be shown that the recently developed perturbation method based onintegrating factors can be used to approximate first integrals. Not onlyapproximations of first integrals will be given, butit will also be shown how in a rather efficient way the existence and stability oftime-periodic solutions can be obtained from these approximations. In particularthe generalized Rayleigh oscillator equation
will be studied in detail, and it will beshown that at least five limit cycles can occur. 相似文献
175.
Suppose that k and l are integers such that
and
, M
k is a set of numbers without kth powers, and
. In this paper, we obtain asymptotic estimates of the sums
over
相似文献
176.
Roman Luis J. Zhang Xinsheng Zheng Weian 《Mathematical Physics, Analysis and Geometry》2003,6(2):113-124
We consider the solutions to /tu
(n)=a
(n)(x)u
(n) where {a
(n)(x)}
n=1,2,... are random fields satisfying a well-mixing condition (which is different to the usual strong mixing condition). In this paper we estimate the rate of convergence of u
(n) to the solution of a heat equation. Since our equation is of simple form, we get quite strong result which covers the previous homogenization results obtained on this equation. 相似文献
177.
The fundamental frequency of a membrane is the square root ofthe lowest eigenvalue of the negative Laplace operator withDirichlet boundary conditions. A doubly connected membrane withthe inner region of vanishing maximal dimension 2c is consideredin this paper. A modified perturbation method is developed toprovide an asymptotic expansion (c 0) for the fundamental frequencyof the membrane. The first three order terms of the asymptoticexpansion for the fundamental frequency of a doubly connectedmembrane with the circular inner region are derived explicitly.The results are compared with the exact solutions and the approximationsdetermined by other investigators. The error of the perturbationcalculations compared with the exact values is less than 1%as c is less than or equal to 0·25 and is less than 4%as c is less than or equal to 0·35. 相似文献
178.
Necessary and sufficient conditions are obtained for every solution of
to oscillate or tend to zero as n , where p
n, q
n and f
n are sequences of real numbers such that q
n 0. Different ranges for p
n are considered. 相似文献
179.
The work is designated for obtaining asymptotic expansions and determination of structures of the remainder terms that take into consideration large deviations both in the Cramer zone and Linnik power zones for the distribution density function of sums of independent random variables in a triangular array scheme. The result was obtained using general Lemma 6.1 of Saulis and Statuleviius in Limit Theorems for Large Deviations (Kluwer, 1991) and joining the methods of characteristic functions and cumulants. The work extends the theory of sums of random variables and in a special case, improves S. A.Book's results on sums of random variables with weights. 相似文献
180.
Mohammed Bellalij 《Numerical Algorithms》2003,33(1-4):65-82
Henrici's transformation is the underlying scheme that generates, by cycling, Steffensen's method for the approximation of the solution of a nonlinear equation in several variables. The aim of this paper is to analyze the asymptotic behavior of the obtained sequence (s
n
*
) by applying Henrici's transformation when the initial sequence (s
n
) behaves sublinearly. We extend the work done in the regular case by Sadok [17] to vector sequences in the singular case. Under suitable conditions, we show that the slowest convergence rate of (s
n
*
) is to be expected in a certain subspace N of R
p
. More precisely, if we write s
n
*
=s
n
*
,N+s
n
*
,N, the orthogonal decomposition into N and N
, then the convergence is linear for (s
n
*
,N) but (
n
*
,N) converges to the same limit faster than the initial one. In certain cases, we can have N=R
p
and the convergence is linear everywhere. 相似文献