Convergence and Limit Theorems for Sequences of Random Variables
Convergence and Limit Theorems for Sequences of Random Variables
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随机变量序列的收敛性和极限定理
DOI：
10.1137/1117049
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发表时间：
1973
影响因子：
0.6
通讯作者：
V. Gapoškin
中科院分区：
文献类型：
--
作者：
V. Gapoškin
弱相依随机变量的性质及其与独立随机变量性质的关系已在许多方面得到了深入的研究。详细的调查已取得的性质的类弱相关序列，如马尔可夫链，鞅，平稳序列等，另一方面，一个重要的地方，在理论的三角和正交级数是heldby所谓的间隙系列（系列关于充分稀疏的子系统的原始系统），其性质类似于那些系列的独立条款。文[1]-[5]及其他文献证明了定义在[0，1]上的标准正交系统{X，}（在适当的限制下）有一个充分稀疏的子系统{X，}，它具有与独立函数系统类似的收敛性、绝对收敛性、可积性和极限性质。
The properties of weakly dependent random variables and their relationship to the properties of independent random variables have been studied intensively in many directions. Detailed investigations have been made of the properties of classes of weakly dependent sequences such as Markov chains, martingales, stationary sequences, etc. On the other hand, an important place in the theory of trigonometric and orthogonal series is heldby the so-called gap series (series with respect to sufficiently sparse subsystems of the original system) which have properties similar to those of series with independent terms. In [1]-[5] and elsewhere, it is shown that an orthonormal system {X,} defined on [0, 1] has (under appropriate restrictions) a sufficiently sparse subsystem {X,} which has properties of convergence, absolute convergence, integrability and limiting properties similar to those of systems of independent functions.