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71.
This paper is concerned with large- error estimates concerning convergence in distribution as well as norm convergence for Banach space-valued martingale difference sequences. Indeed, two general limit theorems equipped with rates of convergence for such difference sequences are established. Applications of these lead to the central limit theorem and the weak law of large numbers with rates for Banach space-valued martingales. 相似文献
72.
In his 1961 paper, Marcel Golay showed how the search for pairs of binary sequences of length with complementary autocorrelation is at worst a problem. Andres, in his 1977 master's thesis, developed an algorithm which reduced this to a search and investigated lengths up to 58 for existence of pairs. In this paper, we describe refinements to this algorithm, enabling a search at length 82. We find no new pairs at the outstanding lengths 74 and 82. In extending the theory of composition, we are able to obtain a closed formula for the number of pairs of length generated by a primitive pair of length . Combining this with the results of searches at all allowable lengths up to 100, we identify five primitive pairs. All others pairs of lengths less than 100 may be derived using the methods outlined.
73.
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
74.
L. O. Jay 《BIT Numerical Mathematics》2001,41(2):422-429
To complement the property of Q-order of convergence we introduce the notions of Q-superorder and Q-suborder of convergence. A new definition of exact Q-order of convergence given in this note generalizes one given by Potra. The definitions of exact Q-superorder and exact Q-suborder of convergence are also introduced. These concepts allow the characterization of any sequence converging with Q-order (at least) 1 by showing the existence of a unique real number q [1,+] such that either exact Q-order, exact Q-superorder, or exact Q-suborder q of convergence holds.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
75.
76.
Fernando Mayoral 《Proceedings of the American Mathematical Society》2001,129(1):79-82
We characterize the compactness of a subset of compact operators between Banach spaces when the domain space does not have a copy of
77.
The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem. 相似文献
78.
We study rate of convergence in the strong law of large numbers for finite and infinite variance time series in both contexts of weak and strong dependence. 相似文献
79.
Ragheb M. Abu-Sarris 《Journal of Computational Analysis and Applications》2000,2(1):103-109
In this paper, we are concerned with the global behavior ofthe solutions of the difference equation
where
and
. Necessary and sufficient conditions for boundedness, persistence,and periodicity of all solutions will be established. The oscillatorybehavior will be investigated. 相似文献
80.
In this paper, we study the central limit theorem and its weak invariance principle for sums of a stationary sequence of random
variables, via a martingale decomposition. Our conditions involve the conditional expectation of sums of random variables
with respect to the distant past. The results contribute to the clarification of the central limit question for stationary
sequences.
Magda Peligrad is supported in part by a Charles Phelps Taft research support grant at the Univeristy of Cincinnati and the
NSA grant H98230-05-1-0066. 相似文献