Shift Self-Similar Additive Random Sequences Associated with Supercritical Branching Processes

Natural examples of increasing shift self-similar additive random sequences are constructed, which are associated with supercritical branching processes. The rate of growth and the distributional properties of them are studied in terms of the offspring distributions of the supercritical branching processes. The results are applied to two types of laws of the iterated logarithm for a Brownian motion on the unbounded Sierpinski gasket. An extension of the Bingham–Doney–de Meyer theorem on the limits of supercritical branching processes is also proved.     

Recurrence-Transience for Self-similar Additive Processes Associated with Stable Distributions

For any stable distribution on the line, recurrence-transience of the selfsimilar additive process {X _t ,t0} with (X ₁)= is determined. Comparison with the stable Lévy process {Y _t ,t0} with (Y ₁)= is made: if is not strictly stable, then {Y _t } is transient but {X _t } is recurrent except the obviously transient case of monotone sample functions.     

Rates of Convergence for Double Sequences

In 1900 Pringsheim presented the following definition for convergence of a double sequence (i.e. ordinary infinite matrices). A double sequence [x] has limit L if the terms of the double sequence approaches L as both the column and row indices increases. Using this notion for convergence I will present definitions for asymptotically equivalent double sequences, rate preserving four dimensional matrix transformation, and these definitions shall be used to present two natural invariance theorems.AMS Subject Classification (2000): Primary 42B15, Secondary 40C05     

Additive Completion of Lacunary Sequences

To the memory of Pál Erdős Thirty years ago I read the following question of Erdőos [4]: "Does there exist a sequence with so that every sufficiently large number is of the form ? $10" I sent my solution to Erdős in a letter (in Hungarian). He translated my letter into English and sent it to the Canadian Math. Bulletin; this became my first paper to appear. In this paper we will find, among others, the best value of the constant c in the above question, which was also asked by Erdős. Received March 30, 2000 RID="*" ID="*" Supported by Hungarian National Foundation for Scientific Research, Grants No. T 025617 and T 29759.     

Kubilius-Type Sequences of Additive Functions

We consider conditions under which the distributions of sequences of integer-valued nonnegative strongly additive functions can be approximated by the distributions of sums of independent random variables.__________Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 2, pp. 270–281, April–June, 2005.     

Finite Subsequences of Shift Register Sequences

In a stream cipher a cryptogram is produced from a binary datastream by modulo-2-adding it to a keystream sequence. The securityof the system relies on the inability of an interceptor to determinethis keystream sequence. One obvious requirement for such asystem is that there should be sufficiently many possibilitiesfor the keystream sequence that the interceptor cannot possiblytry them all. In this paper we consider the likelihood of an interceptor beingable to decipher the cryptogram correctly even though he maybe trying the wrong keystream sequence. This possibility arisesbecause the length of any particular message is likely to beconsiderably shorter than the period of the keystream sequence,and thus only a comparatively small section of the keystreamsequence is used. Hence, if the interceptor tries a sequencewhich intersects (i.e. agrees) with the keystream sequence inthe appropriate positions, he will deduce the message correctly. A number of the standard methods for generating keystream sequencesuse shift registers as ‘building blocks’. So welook in considerable detail at the number of intersections (ofvarious lengths) for sequences generated by two different shiftregisters. We also show that if a keystream sequence has linearequivalence n, then the local linear equivalence of any subsequenceof length at least 2n is n. This means that if the message haslength at least 2n and the keystream sequence has linear equivalencen, then there is no other sequence of linear equivalence lessthan n+1 which can be used to decipher correctly.     

Additive and Multiplicative Expansions in Multidimensional Local Fields

The paper is a continuation of the authors' previous paper on the topology of higher local fields. A useful class of systems of topological generators for the additive and multiplicative groups is described. Bibliography: 3 titles.     

Construction of Pseudorandom Binary Sequences Using Additive Characters

In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large.     

Construction of Pseudorandom Binary Sequences Using Additive Characters

In earlier papers the authors studied finite pseudorandom binary sequences, and they constructed sequences with strong pseudorandom properties. In these earlier constructions multiplicative characters were used. In this paper a new construction is presented which utilizes properties of additive characters. These new sequences can be computed fast, they are well-distributed relative to arithmetic progressions and their correlations of small order are small, but the price paid for the fast computation is that the correlations of large order can be large.     

满秩多维平稳序列对线性系统的滤波问题

本文讨论满秩多维平稳序列对线性系统的滤波问题,给出了平稳序列值空间H_X中任一元ξ的最优滤波的谱特征及滤波误差Q=E|ξ-|~2的表达式。     

多类型复发事件下变系数加性乘积比率回归模型

本文基于多类型复发事件数据,讨论了一个新的加性乘积比率回归模型,该模型包括两部分,其中第一部分为可加Aalen模型,其中协变量影响为加性的且与时间有关.第二部分为Cox回归模型,其中协变量有乘性影响.利用估计方程的方法,给出了该模型中未知参数和非参数函数的一种估计方法,并利用现代经验过程理沦证明了所得估计的相合性和渐近正态性.     

关于若干重要数列的收敛速度及其渐近性

对极限值为重要常数e、π及欧拉常数γ的数列的收敛速度及渐近性进行讨论,我们很惊奇地发现它们当中的大部分数列具有完全相同的收敛速度及其渐近性.     

A Note on Sequences with the Shift and Add Property

A sequence of elements from a finite field satisfies the shift and add property if the componentwise sum of any two shifts of the sequence is either a shift of the sequence or the all zero sequence. A sequence whose elements lie in an arbitrary group satisfies the shift and multiply property if the componentwise product of any two shifts of the sequence is either a shift of the sequence or the all identity sequence. The paper classifies sequences which have the shift and add property or the shift and multiply property.     

A Non-Uniform Estimate in the Central Limit Theorem for Sequences of Strongly Additive Functions

The value distribution of a normalised sequence of strongly additive arithmetic functions

Convergence Rates for Linear Inverse Problems in the Presence of an Additive Normal Noise

Abstract

In this work, we examine a finite-dimensional linear inverse problem where the measurements are disturbed by an additive normal noise. The problem is solved both in the frequentist and in the Bayesian frameworks. Convergence of the used methods when the noise tends to zero is studied in the Ky Fan metric. The obtained convergence rate results and parameter choice rules are of a similar structure for both approaches.     

Galois环上极大周期序列的平移等价

本文给出了Galois环上两个具有相同特征多项式的极大周期序列是否平移等价的—个判定方法,以及在两个序列平移等价的情况下,利用模p方幂提升技术,给出了—个计算它们的平移距离的方法.     

用迹表示研究序列的线性复杂度

本文用迹表示式证明了序列的线性复杂度等于其秩矩阵的秩，并由此导出了正规基的计数公式．