Almost sure central limit theory for products of sums of partial sums

Consider a sequence of i.i.d.positive random variables.An universal result in almost sure limit theorem for products of sums of partial sums is established.We will show that the almost sure limit theorem holds under a fairly general condition on the weight dk= k-1 exp（lnβk）,0≤β〈1.And in a sense,our results have reached the optimal form.

ON THE LIMITING BEHAVIOR OF THE MAXIMUM PARTIAL SUMS FOR ARRAYS OF ROWWISE NA RANDOM VARIABLES

Let {Xni, 1 ≤ n,i 〈 ∞} be an an array of rowwise NA random variables and {an, n ≥ 1} a sequence of constants with 0 〈 an ↑∞ . The limiting behavior of maximum partial sums 1/an max 1≤k≤n｜^k∑i=1 Xni｜ is investigated and some new results are obtained. The results extend and improve the corresponding theorems of rowwise independent random variable arrays by Hu and Taylor [1] and Hu and Chang [2].

SELF-NORMALIZED CENTRAL LIMIT THEOREM AND ESTIMATION OF VARIANCE OF PARTIAL SUMS FOR NEGATIVE DEPENDENT RANDOM VARIABLES

Let ｛X n,n≥1｝ be a stationary LNQD or NA sequence satisfying EX 1=μ,EX 2 1<∞ and (Var S n)/n→σ 2 as n→∞.In this paper a class of self-normalized central limit theorems and estimators of Var S n are studied.The weak and strong consistency of the estimators of Var S n are presented.

On Moments of the Maximum of Normed Partial Sums of ρ^--mixing Random Variables

In this paper, we obtain the moment conditions for the supermun of normed sums of ρ^--mixing random variables by using the Rosenthal-type inequality for Maximum partial sums of ρ^--mixing random variables. The result obtained generalize the results of Chen(2008) and extend those to negatively associated sequences and ρ^--mixing random variables.

On the Limiting Behavior of Weighted Partial Sums for B Valued Martingale Difference Sequences

Let {Xn, n≥1} be a martingale difference sequence and {a nk , 1?k?n,n?1} an array of constant real numbers. The limiting behavior of weighted partial sums ∑ k=1 n a nk X k is investigated and some new results are obtained.

Complete Convergence for Partial Sums of the Squares of ARCH Sequence

In this paper,we discuss the suffcient condition for complete convergence of partial sums of squares of the ARCH sequence,at the same time a moment inequality of maximum partial sums for squares of the ARCH sequence is proved.

Moments of the maximum of normed partial sums of ρ^--mixing random variables

Let {Xn,n ≥ 1} be a sequence of identically distributed ρ^--mixing random variables and set Sn =∑i^n=1 Xi,n ≥ 1,the suffcient and necessary conditions for the existence of moments of supn≥1 ｜Sn/n^1/r｜^p（0 〈 r 〈 2,p 〉 0） are given,which are the same as that in the independent case.

ON UNIFORM APPROXIMATION BY PARTIAL SUMS OF JACOBI SERIES ON ELLIPTIC REGION

In this paper, we discuss the relation between the partial sums of Jacobi serier on an elliptic region and the corresponding partial sums of Fourier series. From this we derive a precise approximation formula by the partial sums of Jacobi series on an elliptic region.

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.

Performance and Complexity Trade-Off between Short-Length Regular and Irregular LDPC

In this paper, both the high-complexity near-ML list decoding and the low-complexity belief propagation decoding are tested for some well-known regular and irregular LDPC codes. The complexity and performance trade-off is shown clearly and demonstrated with the paradigm of hybrid decoding. For regular LDPC code, the SNR-threshold performance and error-floor performance could be improved to the optimal level of ML decoding if the decoding complexity is progressively increased, usually corresponding to the near-ML decoding with progressively increased size of list. For irregular LDPC code, the SNR-threshold performance and error-floor performance could only be improved to a bottle-neck even with unlimited decoding complexity. However, with the technique of CRC-aided hybrid decoding, the ML performance could be greatly improved and approached with reasonable complexity thanks to the improved code-weight distribution from the concatenation of CRC and irregular LDPC code. Finally, CRC-aided 5GNR-LDPC code is evaluated and the capacity-approaching capability is shown.

POSITIVITY AND BOUNDEDNESS OF TRIGONOMETRIC SUMS

We give a systematic account of results which assure positivity and boundedness of partial sums of cosine or sine series. New proofs of recent results are sketched.

A Precise Asymptotic Behaviour of the Large Deviation Probabilities for Weighted Sums

Let {Xn, n ≥ 1} be a sequence of independent and identically distributed positive valued random variables with a common distribution function F. When F belongs to the domain of partial attraction of a semi stable law with index α, 0 < α < 1, an asymptotic behavior of the large deviation probabilities with respect to properly normalized weighted sums have been studied and in support of this we obtained Chover’s form of law of iterated logarithm.

Parallel Computation of Disjoint Products Approach

In this paper, extracting parallelizatio n from the sum of disjoint products approach is discussed. A general framework of parallelizing disjoint products approach is presented. And a parallel version of the newest disjoint products algorithm is implemented. The results of testing s how the effect is so good to get linear speedups.

Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence

Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ（n） =EX1Xn＋1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level （x/√2 log n＋√2 log n-log（4π log n）/2√log n） √1-τ（n） ＋ X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on （0,1].

Generalized Series of Bernoulli Type

The problem of evaluating an infinite series whose successive terms are reciprocal squares of the natural numbers was posed without a solution being offered in the middle of the seventeenth century. In the modern era, it is part of the theory of the Riemann zeta-function, specifically ζ (2). Jakob Bernoulli attempted to solve it by considering other more tractable series which were superficially similar and which he hoped could be algebraically manipulated to yield a solution to the difficult series. This approach was eventually unsuccessful, however, Bernoulli did produce an early monograph on summation of series. It remained for Bernoulli’s student and countryman Leonhard Euler to ultimately determine the sum to be . We characterize a class of series based on generalizing Bernoulli’s original work by adding two additional parameters to the summations. We also develop a recursion formula that allows summation of any member of the class.

Rearrangement Inequality and Chebyshev＇s Sum Inequality on Positive Tensor Products of Orlicz Sequence Space with Banach Lattice

Let φ be an Orlicz function that has a complementary function φ＊ and let lφ be an Orlicz sequence space. We prove a similar version of Rearrangement Inequality and Chebyshev＇s Sum Inequality in lφ FX, the Fremlin projective tensor product of lφ with a Banach lattice X, and in lφ iX, the Wittstock injective tensor product of lφ with a Banach lattice X.

On the Product of Integro Differential Equations and Their Solutions in Direct Sum Spaces

In this paper, we consider a general quasi-differential expressions t1,t2 Tn, each of order n with complex coefficients and their formal adjoints are t1＋,t2＋- x＋ on [0, b） respectively. We show in the direct sum spaces LZ（Ip）, p = 1,2 N of functions defined on each of the separate intervals with the case of one singular end-points and under suitable conditions on the function F that all solutions of the product quasi-integro differential equations are bounded and LZw -bounded on [0,b）.

On the Convergence of Observed Partial Likelihood under Incomplete Data with Two Class Possibilities

In this paper, we discuss the theoretical validity of the observed partial likelihood (OPL) constructed in a Coxtype model under incomplete data with two class possibilities, such as missing binary covariates, a cure-mixture model or doubly censored data. A main result is establishing the asymptotic convergence of the OPL. To reach this result, as it is difficult to apply some standard tools in the survival analysis, we develop tools for weak convergence based on partial-sum processes. The result of the asymptotic convergence shown here indicates that a suitable order of the number of Monte Carlo trials is less than the square of the sample size. In addition, using numerical examples, we investigate how the asymptotic properties discussed here behave in a finite sample.

基于低密度校验码的OFDM编码调制译码算法

低密度校验码(LDPC)具有编码增益高、译码速度快、性能接近Shannon限的优点。LDPC码应用于OFDM,能有效地提高多径环境下OFDM的BER性能。本文首先简单介绍LDPC码及其概率域上的译码算法,在此基础上对译码算法作融合,阐述概率似然比的译码算法。为了把LDPC应用于OFDM系统上,提出了多电平调制下的LDPC译码的算法。仿真结果表明,在AWGN和Rayleigh信道下,此算法正确有效。

OFDM系统中基于因子图的信道估计算法

为提高正交频分复用(OFDM)系统的信道估计精度,根据频谱资源的无线信道特性,提出基于因子图的OFDM系统信道估计算法,包括二维联合信道估计算法和2个级联的一维信道估计算法。将时变频率选择性衰落信道建模为一阶自回归模型,使信道参数之间的交互信息近似为高斯分布,利用和积算法实现OFDM系统的联合信道估计和符号检测。仿真结果表明,该信道估计算法能够以较低的计算复杂度逼近最优的估计性能。