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81.
A distribution function F on the nonnegative real line is called subexponential if limx(1-F
*n
(x)/(1 - F(x)) = n for all n 2, where F
*n
denotes the nfold Stieltjes convolution of F with itself. In this paper, we consider the rate of convergence in the above definition and in its density analogue. Among others we discuss the asymptotic behavior of the remainder term R
n
(x) defined by R
n
(x) = 1 - F*n(x) - n(1 - F(x)) and of its density analogue rn (x) = -(Rn (x))'. Our results complement and complete those obtained by several authors. In an earlier paper, we obtained results of the form n(x) = O(1)f(x)R(x), where f is the density of F and R(x) =
0
x
(1-F(y))dy. In this paper, among others we obtain asymptotic expressions of the form R
n(x)=
2
n
R2(x) + O(1)(-f'(x))R2(x) where f' is the derivative of f. 相似文献
82.
This paper deals with Sturm-Liouville operators generated on a finite interval and on the whole axis by the differential expressionl(y)=−y
"
+q(x)y, whereq(x) is a distribution of first order, such that
. The minimal and maximal operators corresponding to potentials of this type on a finite interval are constructed. All self-adjoint
extensions of the minimal operator are described and the asymptotics of the eigenvalues of these extensions is found. It is
proved that the constructed operator coincides with the norm resolvent limit of the Sturm-Liouville operators generated by
smooth potentialsq
n
, provided that the condition
holds. The convergence of the spectra of these operators to the spectrum of the limit operator is also proved. Similar results
are obtained in the case of the whole axis.
Translated fromMatematicheskie Zametki, Vol. 66, No. 6, pp. 897–912, December, 1999. 相似文献
83.
For nilpotent quantum groups [as introduced by Franz et al.
(7)], we show that (in sharp contrast to the classical case) the symmetrization
of a probability distribution and the first moments of together determine uniquely the original distribution . 相似文献
84.
Pavle Mladenovic´ 《Extremes》1999,2(4):405-419
Let X
n1
*
, ... X
nn
*
be a sequence of n independent random variables which have a geometric distribution with the parameter p
n = 1/n, and M
n
*
= \max\{X
n1
*
, ... X
nn
*
}. Let Z
1, Z2, Z3, ... be a sequence of independent random variables with the uniform distribution over the set N
n = {1, 2, ... n}. For each j N
n let us denote X
nj = min{k : Zk = j}, M
n = max{Xn1, ... Xnn}, and let S
n be the 2nd largest among X
n1, Xn2, ... Xnn. Using the methodology of verifying D(un) and D'(un) mixing conditions we prove herein that the maximum M
n has the same type I limiting distribution as the maximum M
n
*
and estimate the rate of convergence. The limiting bivariate distribution of (Sn, Mn) is also obtained. Let
n, n Nn,
,
and T
n = min{M(An), M(Bn)}. We determine herein the limiting distribution of random variable T
n in the case
n ,
n/n > 0, as n . 相似文献
85.
A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137. 相似文献
86.
Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1992,44(2):363-378
Let X
1, X
2,... be a sequence of nonnegative integer valued random variables.For each nonnegative integer i, we are given a positive integer k
i
. For every i = 0, 1, 2,..., E
i
denotes the event that a run of i of length k
i
occurs in the sequence X
1, X
2,.... For the sequence X
1, X
2,..., the generalized pgf's of the distributions of the waiting times until the r-th occurrence among the events % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaiWabeaacaWGfbWaaSbaaSqaaiaadMgaaeqaaaGccaGL7bGaayzF% aaWaa0baaSqaaiaadMgacqGH9aqpcaaIWaaabaGaeyOhIukaaaaa!43D8!\[\left\{ {E_i } \right\}_{i = 0}^\infty\]are obtained. Though our situations are general, the results are very simple. For the special cases that X's are i.i.d. and {0, 1}-valued, the corresponding results are consistent with previously published results.This research was partially supported by the ISM Cooperative Research Program (90-ISM-CRP-11) of the Institute of Statistical Mathematics. 相似文献
87.
J. A. Cuesta-Albertos C. Matrán-Bea A. Tuero-Diaz 《Journal of Theoretical Probability》1996,9(2):263-283
We provide two families of lower bounds for theL
2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02. 相似文献
88.
This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed. 相似文献
89.
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
90.
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