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1.
Uwe Einmahl 《Probability Theory and Related Fields》1988,77(1):65-85
Summary We obtain a strong approximation theorem for partial sums of i.i.d.d-dimensional r.v.'s with possibly infinite second moments. Using this result, we can extend Philipp's strong invariance principle for partial sums of i.i.d.B-valued r.v.'s satisfying the central limit theorem toB-valued r.v.'s which are only in the domain of attraction of a Gaussian law. This new strong invariance principle implies a compact as well as a functional law of the iterated logarithm which improve some recent results of Kuelbs (1985). 相似文献
2.
A. N. Frolov 《Journal of Mathematical Sciences》2006,133(3):1356-1370
We derive universal strong laws for increments of sums of independent, nonidentically distributed, random variables. These
results generalize universal results of the author for the i.i.d. case which include the strong law of large numbers, law
of the iterated logarithm, Erdos-Renyi law, and Csorgo-Revesz laws. Bibliography: 27 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 311, 2004, pp. 260–285. 相似文献
3.
Phillip S. Griffin 《Probability Theory and Related Fields》1988,78(2):293-319
Summary We study the law of the iterated logarithm for the partial sum of i.i.d. random variables when the r
n largest summands are excluded, where r
n=o(log logn). This complements earlier work in which the case log logn=O(rn) was considered. A law of the iterated logarithm is again seen to prevail for a wide class of distributions, but for reasons quite different from previously.Research supported in part by NSF Grant DMS-8501732 相似文献
4.
A. N. Frolov 《Journal of Mathematical Sciences》2005,128(1):2604-2613
We derive universal strong laws for increments of sums of i.i.d. random variables with multidimensional indices without an exponential moment. Our theorems yield the strong law of large numbers, the law of the iterated logarithm, and the Csorgo-Revesz laws for random fields. New results are obtained for distributions from domains of attraction of the normal law and of completely asymmetric stable laws with index (1, 2). Bibliography: 18 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 298, 2003, pp. 191–207. 相似文献
5.
Daniel Charles Weiner 《Probability Theory and Related Fields》1986,72(3):337-357
Summary When operators T
n exist such that for sums S
n
of n i.i.d. copies of a finite-dimensional random vector X we have T
n
S
n
is shift-convergent in distribution to a standard Gaussian law, a necessary and sufficient condition on the distribution of X is given for the appropriate law of the iterated logarithm using the operators T
n
to hold. Our result extends certain well-known real line L.I.L.'s; it utilizes a necessary and sufficient condition due to Hahn and Klass for T
n
to exist giving a Gaussian limit law, and employs a second moment technique due to Kuelbs and Zinn. 相似文献
6.
Let X
1, X
2,... be independent, but not necessarily identically distributed random variables in the domain of attraction of a normal law or a stable law with index 0 < α < 2. Using suitable self-normalizing (or Studentizing) factors, laws of the iterated logarithm for self-normalized Hanson–Russo type increments are discussed. Also, some analogous results for self-normalized weighted sums of i.i.d. random variables are given. 相似文献
7.
A. Shahmansoorian 《Journal of Mathematical Sciences》2009,161(2):297-307
In this paper, the construction of CLFs for nonlinear systems and a new inverse optimal control law are presented. The construction
of a CLF for an affine nonlinear system is reduced to the construction of a CLF for a simpler system, and a new L
g
V type control law with respect to a CLF is provided. This control law is a generalization of Sontag’s formula and contains
a design parameter. Tuning this parameter gives many suboptimal solutions for the optimization problem. Also, the gain margin
and sector margin of the control law are calculated. Examples are provided to illustrate the main theoretical results of the
paper.
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 61, Optimal
Control, 2008. 相似文献
8.
Henry Teicher 《Journal of Theoretical Probability》1992,5(2):391-405
Conditions are given for almost certain and distribution convergence of self-normalized generalizedU-statistics composed of random variables without particular probabilistic structure. The set of almost certain limit points of some classicalU-statistics is obtained. A variant of theU-statistic involving squares of some of the random variables is also treated. Applications include Martingale differences, stationary sequences, and the classical i.i.d. case where a Marcinkiewicz-Zygmund-type strong law is obtained. 相似文献
9.
Mark Finkelstein Victor M. Kruglov Howard G. Tucker 《Journal of Theoretical Probability》1994,7(3):565-598
We extend results obtained in Kruglov,(7) and Finkelstein and Tucker(3) to obtain necessary and sufficient conditions for convergence in law of random sums of non-identically distributed independent random variables under non-random centering. Thei.i.d. case is also considered for random variables attracted to a stable law. Necessary and sufficient conditions for convergence in law of these random variables under non-random centering, and in some cases, under non-random norming, are also obtained. The distribution functions for the limit laws are determined as well, generalizing results of Robbins.(10)
Supported in part by The State University of New York and United States Information Agency Grant No. IA AEMP69193692. 相似文献
10.
Beifang Chen 《Annals of Combinatorics》2010,13(4):425-452
This is the first one of a series of papers on association of orientations, lattice polytopes, and group arrangements to graphs.
The purpose is to interpret the integral and modular tension polynomials of graphs at zero and negative integers. The whole
exposition is put under the framework of subgroup arrangements and the application of Ehrhart polynomials. Such a viewpoint
leads to the following main results of the paper: (i) the reciprocity law for integral tension polynomials; (ii) the reciprocity
law for modular tension polynomials; and (iii) a new interpretation for the value of the Tutte polynomial T(G; x, y) of a graph G at (1, 0) as the number of cut-equivalence classes of acyclic orientations on G. 相似文献
11.
R.L Vaughn 《Applicable analysis》2013,92(4):337-348
Let L 0(ΩA,P) be the space of equivalent classes of random variables defined on a probability space (Ω,A,P). Let H be the closed subspace of L 0(Ω,A,P) spanned by a sequence of i.i.d. (independent and identically distributed) random variables having the symmetric nondegenerate law F. It is proved that H is linearly homeomorphic to l p for 0<p≤2 if F belongs to the domain of normal attraction of symmetric stable law withexponent p. 相似文献
12.
Let be an i.i.d. sequence of -valued random vectors belonging to the generalized domain of semistable attraction of some nonnormal law. Assume further
that is a sequence of positive integer valued random variables such that for some
for some discrete positive random variable D, where we do not assume that and are independent. Let . Then various laws of the iterated logarithm for the norm of as well as the radial projection onto a unit vector θ are presented. 相似文献
13.
Smoothing the Moment Estimator of the Extreme Value Parameter 总被引:1,自引:0,他引:1
Let {X
n be a sequence of i.i.d. random variables whose common distribution F belongs to the domain of attraction of an extreme value law. A semi-parametric estimator of the extreme value parameter is the Dekkers, Einmahl and de Haan [8] moment estimator. Practical use of this estimator requires the problematic choice of a number k=k(n) of upper order statistics and there are few reliable guidelines for this choice. An averaging or smoothing technique is proposed for this estimator yielding a less volatile function of k which in practice aids estimation. 相似文献
14.
C. Aistleitner I. Berkes R. Tichy 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):3-20
It is known that for any smooth periodic function f the sequence (f(2
k
x))
k≥1 behaves like a sequence of i.i.d. random variables; for example, it satisfies the central limit theorem and the law of the
iterated logarithm. Recently Fukuyama showed that permuting (f(2
k
x))
k≥1 can ruin the validity of the law of the iterated logarithm, a very surprising result. In this paper we present an optimal
condition on (n
k
)
k≥1, formulated in terms of the number of solutions of certain Diophantine equations, which ensures the validity of the law of
the iterated logarithm for any permutation of the sequence (f(n
k
x))
k≥1. A similar result is proved for the discrepancy of the sequence ({n
k
x})
k≥1, where {·} denotes the fractional part. 相似文献
15.
Raoul LePage Krzysztof Podgórski Michał Ryznar 《Probability Theory and Related Fields》1997,108(2):281-298
Summary. We prove almost sure convergence of a representation of normalized partial sum processes of a sequence of i.i.d. random variables
from the domain of attraction of an α-stable law, α<2. We obtain an explicit form of the limit in terms of the LePage series representation of stable laws. One consequence of
these results is a conditional invariance principle having applications to option pricing as well as to resampling by signs and permutations.
Received: 11 April 1994 / In revised form: 5 November 1996 相似文献
16.
Let be an i.i.d. sequence of -valued random vectors belonging to the generalized domain of semistable attraction of some nonnormal law. Assume further
that is a sequence of positive integer valued random variables such that for some
for some discrete positive random variable D, where we do not assume that and are independent. Let . Then various laws of the iterated logarithm for the norm of as well as the radial projection onto a unit vector θ are presented.
(Received 31 January 2000; in revised form 5 April 2000) 相似文献
17.
In this paper the Bayes estimates are constructed for the distribution density of sufficient statistics in the case of a normal
law. The asymptotic properties of these estimates are discussed. These estimates may be used for constructing classification
rules which allow one to solve new classification problems.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 5–13, Perm, 1991. 相似文献
18.
V. N. Nikulin 《Journal of Mathematical Sciences》1995,75(1):1437-1441
We define a method of construction of integral metrics and estimate 1) the rate of convergence in the central limit theorem;
2) the stability of one statistical characterization of the normal law in terms of these metrics.
Translated fromStatisticheskie Metody Otsenivaniya i Proverki Gipotez, pp. 83–89, Perm, 1990. 相似文献
19.
Let X
1, X
2,... denote an i.i.d. sequence of real valued random variables which ly in the domain of attraction of a stable law Q with index 0<1. under=" a=" von=" mises=" condition=" we=" show=" that=" the=" sum=" of=" order=" statistics=">1.>
相似文献
20.
Zoltán Megyesi 《Journal of Theoretical Probability》2002,15(4):973-1005
Max-semistable laws arise as non-degenerate weak limits of suitably centered and normed maxima of i.i.d. random variables along subsequences {k(n)} such that k(n+1)/k(n)c1, in which case the common distribution function F of the i.i.d. random variables is said to belong to the domain of geometric partial attraction of the max-semistable law. We give a necessary and sufficient condition for F to belong to the domain of geometric partial attraction of a max-semistable law and investigate the structure of these domains. We show that although weak convergence does not take place along {n}=, the distributions of the maxima merge together along the entire {n} with a suitably chosen family of limiting laws. The use of merge is demonstrated by almost sure limit theorems, which are also valid along the whole {n}. 相似文献
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