Complete Convergence Properties of the Sums for -mixing Sequences of Random Variables

This paper discusses complete convergence properties of the sums of -mixing random sequences.As a result,we improve the corresponding results of Wu Qunying(2001). And extended the Baum and Katz complete convergence to the case of -mixing random sequences by moment inequality and truncating without necessarily adding any extra conditions.

Strong Law of Large Numbers and Complete Convergence for Sequences of -Mixing Random Variables

We give some theorems of strong law of large numbers and complete convergence for sequences of φ-mixing random variables. In particular, Wittmann＇s strong law of large numbers and Teicher＇s strong law of large nnumbers for independent random variables are generalized to the case of φ -minxing random variables.

Some Convergence Results for Sequences of -mixing Random Variables

In this paper, we will present some strong convergence results for sequences of ψ-mixing random variables. The results for sequences of ψ-mixing random variables generalize the corresponding results for independent random variable sequences without any extra conditions.

Complete Convergence and Weak Law of Large Numbers for <i><span style="text-decoration:overline;">ρ</span></i>-Mixing Sequences of Random Variables

In this paper, the complete convergence and weak law of large numbers are established for ρ-mixing sequences of random variables. Our results extend and improve the Baum and Katz complete convergence theorem and the classical weak law of large numbers, etc. from independent sequences of random variables to ρ-mixing sequences of random variables without necessarily adding any extra conditions.

An Invariance Principle for ρ^--Mixing Random Sequences

在这份报纸，我们建立一个不变性原则为 -- 在某时刻 condition.The 结果下面混合随机的 se quences 改进并且延长吴(2003 ) 的相关结果。

A Note on the Almost Sure Central Limit Theorem for Partial Sums of ρ^(−)-Mixing Sequences

Let be a strictly stationary sequence of ρ?-mixing random variables. We proved the almost sure central limit theorem, containing the general weight sequences, for the partial sums , where , . The result generalizes and improves the previous results.

SOME LIMIT THEOREMS FOR SEQUENCES OF PAIRWISE NQD RANDOM VARIABLES

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.

CONVERGENCE RATES IN THE STRONG LAWS OF NONSTATIONARYρ~*-MIXING RANDOM FIELDS

By using a Rosenthal type inequality established in this paper, the complete convergence and almost sure summability on the convergence rates with respect to the strong law of large numbers are discussed for *-mixing random fields.

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=1 aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.

Hájek-Rényi-type Inequality for a Class of Random Variable Sequences and Its Applications

In this paper, we obtain the Hejek-Renyi-type inequality for a class of random variable sequences and give some applications for associated random variable sequences, strongly positive dependent stochastic sequences and martingale difference sequences which generalize and improve the results of Prakasa Rao and Soo published in Statist. Probab. Lett., 57（2002） and 78（2008）. Using this result, we get the integrability of supremum and the strong law of large numbers for a class of random variable sequences.

Pseudo-Random Sequences Generator Based on Discrete Hyperchaotic Systems

We first design a discrete hyperchaotic system via piece-wise linear state feedback. The states of the closed loop system are locally expanding in two directions but absolutely bounded on the whole, which implies hyperchaos. Then, we use three suchlike hyperchaotic systems with different feedback gain matrices to design a pseudo-random sequence generator (PRSG). Through a threshold function, three sub-sequences generated from the output of piecewise linear functions are changed into 0-1 sequences. Then, followed by XOR operation, an unpredictable pseudo-random sequence (PRS) is ultimately obtained. The analysis and simulation results indicate that the PRS, generated with hyperchaotic systems, has desirable statistical features.

Permutation and Complementary Algorithm to Generate Random Sequences for Binary Logic

Randomness number generation plays a key role in network, information security and IT applications. In this paper, a permutation and complementary algorithm is proposed to use vector complementary and permuta-tion operations to extend n-variable Logic function space from 22n functions to 22n * 2n! configurations for variant logic framework. Each configuration contains 2n functions can be shown in a 22n-1*22n-1 matrix. A set of visual results can be represented by their symmetric properties in W, F and C codes respec-tively to provide the essential support on the variant logic framework.

Complete Convergence for Weighted Sums of φ-mixing Sequence

In this paper, the complete convergence and strong law of large numbers for weighted sums of φ-mixing sequence with different distribution are investigated under some weaker moment conditions. Our results extend ones of independent sequence with identical distribution to the case of φ-mixing sequence with different distribution.

HIERACHICAL STRUCTURES FOR GENERATING PSEUDO-RANDOM SEQUENCES AND ARRAYS

This paper proposes new hierarchical structures for generating pseudorandom sequences and arrays. The principle of the structures is based on a new concept-multi-interleaving. It is the generalization of normal sequence decimation(sampling). The kernal of the structures is a lower speed linear feedback shift register together with several high speed time-division multiplexers arranged hierarchically. These new structures have much higher speed compared with that of other schemes proposed before.

Limiting Distribution of Extreme Values for FGM Random Sequences

主要， FGM 随机的 sequences.We 的学习极端价值由 FGM 序列的依赖结构证明一条技术定理，并且进一步获得限制的这份报纸最大值和为静止 FGM 随机的序列最大的 k-th 的分布。

Complete Convergence for Arrays of Rowwise Ч-mixing Random Variables

In the paper, the complete convergence for arrays of rowwise φ-mixing random variables is studied. Some sufficient conditions for complete convergence for an array of rowwise φ-mixing random variables without assumptions of identical distribution and stochastic domination are presented.

LARGE DEVIATIONS FOR SOME DEPENDENT SEQUENCES

Let （Xi） be a martingale difference sequence and Sn=∑^ni=1Xi Suppose （Xi） i=1 is bounded in L^p. In the case p ≥2, Lesigne and Volny （Stochastic Process. Appl. 96 （2001） 143） obtained the estimation μ（Sn 〉 n） ≤ cn^-p/2, Yulin Li （Statist. Probab. Lett. 62 （2003） 317） generalized the result to the case when p ∈ （1,2] and obtained μ（Sn 〉 n） ≤ cn^l-p, these are optimal in a certain sense. In this article, the authors study the large deviation of Sn for some dependent sequences and obtain the same order optimal upper bounds for μ（Sn 〉 n） as those for martingale difference sequence.

Evolutionary Random Sequence Generators Based on LFSR

Random numbers play a crucial role in modern security schemes. Couple to the rapid development of cryptography, the strength of security protocols and encryption algorithms consumingly relies on the quality of random number. With simple architecture and faster speed, linear feedback shift register often is selected in many applications. However, the random sequence generated by LFSR can not meet the demand of unpredictability for secure mechanism. Genetic algorithm improves the linear property of LFSR and constructs a novel random sequence generator with longer period and complex architecture.

SOME SMALL DEVIATION THEOREMS FOR ARBITRARY CONTINUOUS RANDOM SEQUENCE

Let （Xn）n∈EN be a sequence of arbitrary continuous random variables, by the notion of relative entropy hμ^μ（w） as a measure of dissimilarity between probability measure # and reference measure μ, the explicit, general bounds for the partial sums of arbitrary continuous random variables under suitable conditions are developed. The argument uses the known and elementary lcmma of convergence for likelihood ratio.

2D Conjugate Maps of DNA Sequences

Random sequences play an important role in wider security applications, such as mobile communication and network security. Due to DNA sequences owning natural randomness, in order to show DNA’s characteristics intuitively, this paper proposes a method to present DNA sequences as conjugate maps. The method includes two core models: measuring models to transfer DNA data into measurements, and visual models to test random sequences as distribution maps to show DNA’s characteristics. The spatial relations between sample DNA and CA random sequences are illustrated and compared in the end. The results show that the distribution of DNA sequences and CA random sequences has significant differences and similarities. It can provide a reference for in-depth visualization study of DNA sequences on their measurement maps.