马修斯的计算利用了这样一条定理：对于任意一群随机数的大集合，任意两个数没有公约数的概率为6/pi2。
Matthews used the fact that for any large collection of random numbers, the probability that any two have no common factor is 6/pi2.
在证明中采用了一种把网微分法与条件矩母函数相结合应用于随机选择系统强极限定理研究的一种途径。
In the proof, the tools of the conditional moment generating function and the differentiation on a net for the study on strong limit theorems in the random selection system are applied.
本文研究了离散型随机变量次序统计量的分布矩阵的对称性，获得了二个定理。
In this paper, we study the symmetry on distribution matrix of order statistic of discrete type random variable. Therefore, we obtain two theorems.
本文研究了负相协随机变量列极限定理的若干问题。
In this article, we investigate some problems of the limit theorems of the NA random variables.
在可测模糊随机函数及模糊值函数积分的基础上，研究了模糊值函数的有界控制收敛定理。
This paper gives the control convergent theorem of integral for fuzzy random functions on basis fuzzy functions and fuzzy integral.
本文根据的一个数学定理，对受多个物理白噪声激励的极一般的一个自由度系统导出了随机平均方程。
Based on a theorem due to Hasminskii, a stochastic averaging equation is derived for a general system with one degree of freedom subject to physical white noise excitations.
得到了任意随机变量序列的收敛性定理。
A convergence theorem for the sequence of arbitrary random variables is obtained.
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。
In this paper, we establish a class of local convergence theorems for partial sums of arbitrary stochastic adapted sequences which extend some new published results.
讨论了强平稳NA序列的随机指标中心极限定理，给出其成立的一个充分条件。
A sufficient condition of the central limit theorem is given for strongly stationary NA random variables.
本文引进(JM)型算子的概念，并证明非线性增生算子和(JM)型算子随机方程的解的存在定理。
In this paper the concept of operators of type (JM) is introduced and the existence theorems for nonlinear random operator equations of accretive type and of type (JM) are proved.
本文用随机积分的控制收效定理直接推出了这一结果，从而大大简化了原证明。
In the present note we propose to deduce this result directly from the dominated convergence theorem of stochastic integrals, so our proof is much simpler than the original one.
本文研究了离散型随机变量次序统计量的分布矩阵的对称性，获得了二个定理。
In this paper, we study the symmetry on distribution matrix of order statistic of discrete type random variable.
随机不动点定理在随机泛函分析中起重要作用。
Random fixed point theorems are of fundamental importance in probabilistic functional analysis.
其中关于均方全微分和均方方向导数的定理是多指标随机过程所特有的结论。
Four of them, i. e. the theorems on the mean-square total differential and mean-square directional derivative are special conclusions of the multiple parameter stochastic processes.
证明了与随机控制问题有关的动态规划方程粘性解的比较定理。
This paper gives a proof of a comparison theorem on the viscosity solution of HJB Equation.
它的主要理论基础是概率论中的大数定理，其主要手段是随机变量的抽样。
Its main theoretical base is the law of large Numbers in the theory of probability, whose main means is the sampling of random variable.
本文研究了随机环境中耦合空间上不变测度存在性问题，证明了一些存在性定理。
The exist of invariant measure in coupling space of random environments is studied in this paper.
本文作为平稳集值随机过程的表示定理的应用，证明了平稳集值随机过程的遍历性定理。
In this paper, we prove the ergodic theorem of a stationary set valued stochastic process by the representation theorem.
绝对连续随机变量列的记录次数的计数过程的矩精确完全收敛性的一般化定理。
The paper gives the quadrature's precision and complete convergence general theorem, which is about the i.
本文裒集概率论、数理统计、随机过程若干定理的简捷证法，共五款。
This article presents five concise proofs of theorems on probability theory, mathematical statistics and stochastic processes. The proofs are more comprehensible and simpler than conventional ones.
依据中心极限定理，用均匀分布随机数求和的方法得到趋于高斯分布的白噪声。
White noise tending to Gaussian distribution is implemented by summing uniformly distributed random numbers according to the central limit theorem.
当受控对象各控制通路中滞后时间间隔都相同，且输入为随机信号时，可采用二次函数型最优控制定律和分离定理。
The interval of the time lag is identical of each lane controlled and when the input is a random sign, we can adopt quadratic function of optimum control and separation theorem.
最后证明基于双重随机样本的统计学习理论的关键定理并讨论学习过程一致收敛速度的界。
Finally the key theorem of statistical learning theory based on random rough samples is proved, and the bounds on the rate of uniform convergence of learning process are discussed.
对于改进型中心极限定理法，用概率密度转换器对均匀分布的随机数做密度转换，然后再累加产生正态分布的随机数。
With new Central Limit Theorem, convert the uniform random number's probability density using probability density Converter, then add all generated random Numbers.
本文利用随机收缩，证明具有随机定义域的非线性随机算子方程组的解的存在与唯一性定理，给出非线性随机积分和微分方程组的某些应用，改进和推广了某些结果。
In this paper, several existence and uniqueness theorems of solutions are proved for the system of nonlinear random operator equations with stochastic domain by using general random contraction.
根据中心极限定理，以随机数为基础，设计了正态随机变量的结构公式，其数学期望和方差可任意给定。
On the basis of random numbers, The structure-formula of the normal random variable has been designed according to the limit theorem.
第一章，建立了伊藤随机泛函微分方程的一些基本定理。
In Chapter 1, some basic theories of stochastic functional differential equations of Ito-type are developed.
以伪均匀随机数为基础，根据大数中心极限定理，产生高斯分布随机数。
Based on pseudo random uniformity number and the central limit theory of great numeral, random Numbers of Gaussian distribution are produced.
本文主要研究随机递归树和随机二叉搜索树上与分支和子树相关的极限定理。
Some limit laws for the branches and subtrees in a random recursive tree and binary search tree are established in this dissertation.
本文主要研究随机递归树和随机二叉搜索树上与分支和子树相关的极限定理。
Some limit laws for the branches and subtrees in a random recursive tree and binary search tree are established in this dissertation.
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