1) weak law of large numbers
弱大数定律
1.
A weak law of large numbers for the weighted sums of non-identically distributed NA random matrix sequences is studied.
研究了不同分布NA序列加权和最大值的弱大数定律,推广了前人的结果。
2.
In this paper we study the randomly indexed partial sums for arrays 1/(bn) sum from i=1 to Nn ani(Xni-E(XniI(|Xni|≤bn)|Fn,i-1)) under general conditions and establish the weak law of large numbers about it.
在较一般的条件下研究了加权阵列的随机指标部分和1/(bn) sum from i=1 to Nn ani(Xni-E(XniI(|Xni|≤bn)|Fn,i-1))的弱大数定律,其中{Xni,i≥1,n≥1}为随机变量阵列,{Nn,n≥1}是正整数值的随机变量,{bn,n≥1}是正的常数。
3.
It is obtained that the sufficient condition for the Euler s sums of a sequence of separable Bvalued random elements satisfying the weak law of large numbers in this paper.
得到了可分Ｂ值随机元序列的Ｅｕｌｅｒ弱大数定律成立的充分条件。
2) weak law of large number
弱大数定律
1.
A weak law of large number of martingale difference sequence;
鞅差序列的一个弱大数定律
2.
Utilizing some important probability inequation,the author proves the weak law of large numbers and convergence in L~p under the Cesáro uniform integrable conditions,improves and extends some corresponding results.
利用一些重要的概率不等式,在Cesáro一致可积的条件下研究两两NQD列的弱大数定律及Lp的收敛性,改进和推广了一系列的相应结果。
3.
When 1<p≤2,convergence of B valued random fields in Banach spaces is studied,obtained weak law of large numbers and convergence rate for B valued random fields in Banach spaces.
讨论了多指标B值随机变量族{Xn,n∈Zr+}当1弱大数定律及其收敛速度。
3) the weak law of large numbers
弱大数定律
1.
The α-SUE avoids the deficiencies of the conventional stochastic user equilibrium(SUE) that are led by the weak law of large numbers and its equilibrium condition is formulated by variational inequalities.
-αSUE避免了常规的随机用户平衡(SUE)道路选择模型中运用弱大数定律带来的缺陷,其平衡条件用变分不等式来表示。
2.
This paper considers the sum of partial sums of PA sequences which is identically distributed,and the weak law of large numbers is established,thus we can give some references and comparison with I.
本文主要研究了同分布PA序列{Xn}的部分和之和Tn的弱大数定律,与I。
4) week laws of large numbers
弱大数定律
1.
We set up week laws of large numbers by using the uniform bounded condition.
利用一致有界条件,建立弱大数定律,改进了目前的某些结果,并找到弱大数定律与强大数定律的内在差别。
2.
The theorems presented in this paper not only improve former results,but that also receive the difference between the week laws of large numbers and the strong laws of large numbers.
利用一致有界条件,建立了弱大数定律和强大数定律。
5) weak law of large numbers in stochastic sense
随机弱大数定律
1.
sufficient and necessary conditions for weak law of large numbers in stochastic sense are given.
本文讨论随机大数定律 ,得到随机变量序列服从随机弱大数定律的充要条件。
6) weak laws of large numbers
弱大数律
1.
Let {Xn,n≥1} be independent random variables in a real separable Banach space,and the Chung-Teicher type conditions for the SLLN under the assumptions that the weak laws of large numbers hold were doscissed,which is b-1n∑nk=1(Xk-EXkI(‖Xk‖≤bk))p0 holds if and only if b-1n∑nk=1(Xk-EXkI(‖Xk‖≤bk))a.
设{Xn,n≥1}是实可分Banach空间独立随机变量,讨论了在弱大数律的假设下使得Chung-Teicher型强大数律也成立,即bn-1∑nk=1(Xk-EXkI(‖Xk‖≤bk))p0当且仅当bn-1∑nk=1(Xk-EXkI(‖Xk‖≤bk))a。
2.
Chapter 1 Chung-Teicher type SLLN in general Banach spaceIn this chapter,we show that Chung-Teicher type conditions for SLLN under the assumption that the weak laws of large numbers holds.
第一章 Banach空间Chung-Teicher型强大数律 在该章中讨论了在Banach空间中,独立随机变量在弱大数律的假设下,即Chung-Teicher条件下,强大数律也成立。
补充资料：大数定律
| 大数定律 large number，laws of 概率论中讨论随机变量序列的算术平均值向常数收敛的定律。概率论与数理统计学的基本定律之一。又称弱大数理论。例如，在重复投掷一枚硬币的随机试验中，观测投掷n次硬币中出现正面的次数。不同的n次试验，出现正面的频率（出现正面次数与n之比）可能不同，但当试验的次数n越来越大时，出现正面的频率将大体上逐渐接近于1／2。又如称量某一物体的重量，假如衡器不存在系统偏差，由于衡器的精度等各种因素的影响，对同一物体重复称量多次，可能得到多个不同的重量数值，但它们的算术平均值一般来说将随称量次数的增加而逐渐接近于物体的真实重量。由于随机变量序列向常数的收敛有多种不同的形式，按其收敛为依概率收敛，以概率 1 收敛或均方收敛，分别有弱大数定律、强大数定律和均方大数定律。常用的大数定律有：伯努利大数定律、辛钦大数定律、柯尔莫哥洛夫强大数定律和重对数定律。 |
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