随机函数

Suppose is two-dimension random variable, if there is nonnegative, for arbitrary real value such that

则称是二维连续型随机变量，函数称为二维连续型随机变量的分布密度，或称为的联合密度。

Finally, a stochastic averaging method based on generalized harmonic functions has been introduced and applied to the study of dynamics of Brownian particles.

最后，本文介绍了一种基于广义谐和函数的随机平均法，并将它初步应用于受宽带噪声激励下的Brown粒子随机运动系统的研究。

Both the fuzziness and the randomness of the basic variable and the state variable are considered in the present method.

结合工程实际，提出了非闭合隶属函数的截断可能性分布模型，并对模糊强度和模糊应力进行截断处理，给出了结构模糊随机失效概率随截断参数的分布，并给出了结构模糊随机失效概率分布的数值计算方法。

If the stochastic process {X,t∈R1} is transformed by a bounded Borel measurable function f, then we will obtain a new stochastic process which denotes by Y, namelyY=fX

如果该随机过程{X，t∈R1}被一有界Borel可测函数f变换，则得到新的随机过程，记为Y=fX

If mark the probability density function of continuous random variable X and continuous random variable leave each other, then when,there is , there is inverse function of .

Theorem 如果将连续型随机变量和连续型随机变量的概率密度函数分别记为，则时有：，这里是的反函数。

And then the approach is extended to continuous random variable. The optimal rule of general group decision-making is drawn by the new approach, which turns out to be a generalized weighted majority rule. The weight allocated to a decision-maker should be equal to the information quantity he provides.

鉴于Boltzmann—Shannon熵难以直接用来度量群体决策中信息的变动情况，我们提出了一种对离散随机变量的新的信息度量方法，证明了该信息函数仍然满足等状态时信息量最小这一性质；随后将其推广到了连续随机变量。

Thirdly, the problems of institution investor'optimal liquidation strategy and optimal liquidation time were investigated with the conditions that the price of risky asset followed arithmetic Brown motion and liquidation velocity was limited. The problems involved the following scenes: price impact function was linear expression of liquidation velocity which was boundary closed set with an isolated point; price impact function was stochastic; price impact function was nonlinear.

接着，当风险资产的价格服从算术布朗运动，且对投资者的变现速度做出限制时，研究机构投资者的最优变现策略和最优变现时间问题，其中包括：价格冲击函数为变现速度的线性函数，变现速度是一带有孤立点的有界闭集；价格冲击是随机形式；价格冲击是变现速度的非线性函数。

First, the anthor gives a new algorithm of monad distribution function. Under given level, this distribution function can pass Kolmogorov criterion, thus it can approximate samples real distribution function.

首先给出了构造一维随机变量的分布函数的方法：用这种方法构造的分布函数在给定的水平下可通过柯尔莫哥洛夫检验，从而可很好的逼近母体之真实分布函数。

It is also proved that the class of monotone increase functions is PAC solvable under a GA with reproduction and random mutation.

本文还证明了对于由复制和一个按顺序的变异构成的遗传算法，严格单增的函数是PAC可解的，单峰函数是非PAC可解的；对于由复制和随机变异构成的遗传算法，严格单增函数是PAC可解的。

Each generator offers a piecewise linear supply function, within his capacity of generation, into the market and wishes to maximize his expected profit.

当电力市场需求函数表示为市场价格与有界随机需求冲击的非线性函数时，每个发电商在其发电容量范围内向电力市场提交一个分段线性供应函数，以获取最大化利润。

On the other hand, the more important thing is because the urban housing is a kind of heterogeneity products.

另一方面，更重要的是由于城市住房是一种异质性产品。

Climate histogram is the fall that collects place measure calm value, cent serves as cross axle for a few equal interval, the area that the frequency that the value appears according to place is accumulated and becomes will be determined inside each interval, discharge the graph that rise with post, also be called histogram.

气候直方图是将所收集的降水量测定值，分为几个相等的区间作为横轴，并将各区间内所测定值依所出现的次数累积而成的面积，用柱子排起来的图形，也叫做柱状图。