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41.
Ju¨rg Hu¨sler 《Extremes》1999,2(1):59-70
Consider a triangular array of standard Gaussian random variables {n,i, i 0, n 1} such that {n,i, i 0} is a stationary normal sequence for each n 1. Let n,k = corr(n,i,n,i+k). If (1-n,k)log n k (0,) as n for some k, then the locations where the extreme values occur cluster and the limiting distribution of the maxima is still the Gumbel distribution as in the stationary or i.i.d. case, but shifted by a parameter measuring the clustering. Triangular arrays of Gaussian sequences are used to approximate a continuous Gaussian process X(t), t 0. The cluster behavior of the random sequence refers to the behavior of the extremes values of the continuous process. The relation is analyzed. It reveals a new definition of the constants H
used for the limiting distribution of maxima of continuous Gaussian processes and provides further understanding of the limit result for these extremes. 相似文献
42.
Mikael Raab 《Extremes》1999,1(3):295-321
Consider a finite sequence of Gaussian random variables. Count the number of exceedances of some level a, i.e. the number of values exceeding the level. Let this level and the length of the sequence increase simultaneously so that the expected number of exceedances remains fixed. It is well-known that if the long-range dependence is not too strong, the number of exceeding points converges in distribution to a Poisson distribution. However, for sequences with some individual large correlations, the Poisson convergence is slow due to clumping. Using Steins method we show that, at least for m-dependent sequences, the rate of convergence is improved by using compound Poisson as approximating distribution. An explicit bound for the convergence rate is derived for the compound Poisson approximation, and also for a subclass of the compound Poisson distribution, where only clumps of size two are considered. Results from numerical calculations and simulations are also presented. 相似文献
43.
Paul Deheuvels 《Journal of multivariate analysis》1983,13(2):257-272
A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models. 相似文献
44.
Wim Vervaat 《Stochastic Processes and their Applications》1973,1(4):317-334
Weak and strong functional limit theorems are obtained for record values and record epochs in a sequence of independent random variables with common distribution F. The emphasis is on the case in which F is concentrated on the non-negative integers. For contrast, the well-known case of continuous F is also considered. Analogues of results obtained earlier by Resnick, de Haan and the author for continuous F are presented here for F concentrated on the non-negative integers. Also is investigated under which circumstances the latter case is so close to the continuous F case that the resulting limit theorems are the same. 相似文献
45.
Matti Jutila 《Journal of Number Theory》2004,108(1):157-168
Let Hj(s) be the Hecke L-function attached to the Maass wave form for the jth eigenvalue of the hyperbolic Laplacian acting in the Hilbert space of automorphic functions for the full modular group. The following mean value estimate for the central values is proved:
46.
Ming-baoSun Xiao-pingYang 《应用数学学报(英文版)》2004,20(1):123-132
For a Carnot group G,we establish the relationship between extended mean values and r-convexfunctions which is introduced in this paper,which is a class of inequalities of Hadamard type for r-convexfunction on G. 相似文献
47.
Emanuela Caliceti 《Czechoslovak Journal of Physics》2003,53(11):999-1005
Let H be any PT-symmetric Schrödinger operator of the type H=-
2
+x
2
+igW(x), where W is a real polynomial, odd under reflection of all coordinates, gR, acting on L
2
(
R
d
). The proof is outlined of the following statements: PH is self-adjoint and its eigenvalues coincide with the eigenvalues of (H*H). Moreover the eigenvalues of (H*H), known as the singular values of H, can be computed via perturbation theory by Borel summability. 相似文献
48.
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
49.
Baha-Eldin Khaledi Subhash Kochar 《Annals of the Institute of Statistical Mathematics》2001,53(3):620-630
Consider a multivariate mixture model where the random variables X
1, ..., X
n
given (1, ...,
n
), are conditionally independent. Conditions are obtained under which different kinds of positive dependence hold among X
i
's. The results obtained are applied to a variety of problems including the concomitants of order statistics and of record values; and to frailty models. 相似文献
50.
N. Stevanović D. Nikezić 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2007,42(3):397-406
Collision of swift ions with atoms was considered in this paper. The
projectile and target atoms were modeled as assemblies of quantum
oscillators and it was assumed that both, target and projectile could be
excited or ionized, without charge exchange. The model presented here is an
extension of the one given by Sigmund and Haagerup [Phys. Rev. A 34, 892 (1986)]. The number of electrons bound to the projectile, as a function of the projectile velocity,
was used from Cabrera-Trujillo et al. [Phys. Rev. A 55, 2864 (1997)]. Contributions to energy loss from excitation of the projectile and targets were separately considered. It
has been found that projectile excitation contributes up to 20% to the
total energy loss in the lower energy region. Comparisons with other
authors, including SRIM 2003, are also given and good agreement was found. 相似文献