一类随机适应序列部分和的局部极限定理的一个注记

研究了一类随机适应序列的强极限定理,推广了最近发表的几个结果,并进一步推广了Borel—Cantelli引理．     

A class of strong limit theorems for countable nonhomogeneous Markov chains on the generalized gambling system

In this paper, we study the limit properties of countable nonhomogeneous Markov chains in the generalized gambling system by means of constructing compatible distributions and martingales. By allowing random selection functions to take values in arbitrary intervals, the concept of random selection is generalized. As corollaries, some strong limit theorems and the asymptotic equipartition property (AEP) theorems for countable nonhomogeneous Markov chains in the generalized gambling system are established. Some results obtained are extended.      

On the almost everywhere convergence for arbitrary stochastic sequence

The purpose of this paper is to establish a class of strong limit theorems for arbitrary stochastic sequences. As corollaries, we generalize some known results.     

关于B值随机元序列的强收敛性

利用截尾方法构造几乎处处收敛的指数鞅，用鞅方法与分析方法相结合，研究了B值适应可积随机元序列的局部收敛性及其强大数定理．     

关于任意随机适应序列部分和的一类局部极限定理

研究任意随机适应序列部分和的一类局部极限定理,推广了最近发表的几个结果．     

Little's theorem: A stochastic integral approach

In a previous paper we have given a unified approach to the PASTA and the conditional PASTA property that is based upon the observation that the difference between the two limits can be represented as a stochastic integral with respect to a square integrable martingale. The equality of the two limits is then a consequence of a strong law of large numbers for martingales. In this paper we derive a non-standard version of Little's theorem via the same method. The moral of the story is that each of these theorems is but a particular case of a more general theory.     

Weak convergence of partial sums of absolutely regular sequences

We show that weak convergence results for partial sums of absolutely regular sequences can easily be derived from the corresponding convergence results for independent triangular arrays. The link to be used is a simple lemma on the total variation norm.     

关于NA列乘积和强收敛性的注记

讨论了NA随机变量序列乘积和的强收敛性,将王定成等(2002)关于NA列的广义Jam ison型加权和的几乎处处收敛性的结论推广到加权乘积和的强收敛性.     

可积适应随机序列的变换及其a.s.收敛性

引入任意可积适应随机变量序列的停时变换的概念，利用软方法与分析方法相结合，讨论了变换的局部收敛性．作为应用，研究了适随机序列的无规则性定理。     

ND序列部分和的大偏差和强收敛性

利用ND随机变量序列的矩不等式、极大值不等式以及随机变量的截尾方法,重点研究了ND随机变量序列部分和的大偏差结果和强收敛性,推广了文献中一些相依随机变量序列的若干相应结果.     

PA序列部分和完全收敛性的进一步探讨

通过讨论矩的存在性与部分和尾概率级数收敛性的关系,给出了PA序列部分和的完全收敛性,获得了PA序列与独立序列类似的强极限性质.     

Almost convergence and a core theorem for double sequences

The idea of almost convergence was introduced by Moricz and Rhoades [Math. Proc. Cambridge Philos. Soc. 104 (1988) 283-294] and they also characterized the four dimensional strong regular matrices. In this paper we define the M-core for double sequences and determine those four dimensional matrices which transform every bounded double sequence x=[x_jk] into one whose core is a subset of the M-core of x.     

A note on rates of convergence in the multidimensional CLT for maximum partial sums

In this note we obtain rates of convergence in the central limit theorem for certain maximum of coordinate partial sums of independent identically distributed random vectors having positive mean vector and a nonsingular correlation matrix. The results obtained are in terms of rates of convergence in the multidimensional central limit theorem. Thus under the conditions of Sazonov (1968, Sankhya, Series A30 181–204, Theorem 2), we have the same rate of convergence for the vector of coordinate maximums. Other conditions for the multidimensional CLT are also discussed, c.f., Bhattachaya (1977, Ann. Probability 5 1–27). As an application of one of the results we obtain a multivariate extension of a theorem of Rogozin (1966, Theor. Probability Appl. 11 438–441).     

小波级数的部分和的逐点收敛性

对小波级数的部分和的逐点收敛性进行了讨论,通过引入函数空间L2r(R),研究了函数f∈L2r(R)的小波级数的部分和fn的r阶导数对f(r)的逐点逼近问题.当函数f(r)在点x处连续时,建立了逼近速度的一个精确估计,进而得到了相关的逐点收敛定理.其次,当点x为函数f(r)的第一类间断点时,建立了f(r)n对f(r)在点x处的左右极限的算术平均值的收敛速度的一个估计.     

A comparison theorem and uniqueness theorem of backward doubly stochastic differential equations

In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs). We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.     

Generalizations of the Riesz convergence theorem for Lorentz spaces

Summary We obtain preservation inequalities for Lipschitz constants of higher order in simultaneous approximation processes by Bernstein type operators. From such inequalities we derive the preservation of the corresponding Lipschitz spaces.     

Multi-dimensional reflected backward stochastic differential equations and the comparison theorem

In this article, we study the multi-dimensional reflected backward stochastic differential equations. The existence and uniqueness result of the solution for this kind of equation is proved by the fixed point argument where every element of the solution is forced to stay above the given stochastic process, i.e., multi-dimensional obstacle, respectively. We also give a kind of multi-dimensional comparison theorem for the reflected BSDE and then use it as the tool to prove an existence result for the multi-dimensional reflected BSDE where the coefficient is continuous and has linear growth.