随机函数

Under frame of general sum stochastic game theory multi-agent Q-learning method is addressed, we gave the learning function and specific learning algorithm of multi-agent Q-learning.

基于一般和随机对策理论框架下提出了多智能体Q-learning方法，给出了多智能体Q-learning的学习函数以及具体的学习算法。

For the coordination of multiple agents in noncooperation environment, we considered the learning aim as finding a Nash equilibrium strategy through in learning function taking other agent's actions into account. Therefore, we expended the single agent Q-learning algorithm into multiagent Q-learning algorithm. In addition, we proved the convergence of multi-agent Q-learning algorithm under certain general sum stochastic game architecture for only one Nash equilibrium or multiple same Nash equilibrium.

对于非合作环境下的多智能体协调我们通过在学习函数中考虑了智能体的联合行动，提出把学习目标作为求取一个Nash平衡点策略，这样将单智能体Q-learning算法扩展到多智能体的Q-learning算法；证明了在一定的一般和随机对策结构下具有一个或多个相同Nash平衡点条件下多智能体Q-learning算法的收敛性。

It is proved that the doubly stochastic matrix model of G-functions is complete in terms of the state transition's uniformity.

文中证明了转移函数的双随机矩阵数学模型就状态转移过程的均匀性来说是完备的。

The first one focuses upon the fundamental theory and methods of system identification, including the basic concepts of system description and identification,review of matrix theory, stochastic process and pulse response of linear systems; the first principle models for lumped and distributed parameter systems; modeling of bioreactions; auto regressive moving average model; weighted least square and regressive weighted least square for parameter estimation of ARMA model; Runge-Kutta and Simplex methods; an example of BPNN application; as well as Kalman Filter.

第一部分包括知识驱动建模、数据驱动建模、参数估计和状态估计的基础理论和方法。具体为：(1)系统辨识和系统描述的基本概念，包括矩阵论、随机过程、线性系统的脉冲响应函数等基础知识回顾；(2)基于动态物料和能量衡算的集总参数、分布参数对象的知识驱动建模方法；(3)生物反应系统的建模方法；(4)自回归移动平均模型；(5) ARMAX模型参数的加权最小二乘参数估计一次性算法和递推算法，相应的统计性质；(6)龙格库塔法和单纯形法；BP神经网络应用实例；(7)卡尔曼滤波器，及其与加权最小二乘参数估计递推算法的对比。

There are two widely-used inventory service-level measuring func- tions in the stochastic inventory model,i.e,the average stockout per unit time F_1and average outstanding backorders F_2.

在随机存贮模型中有两个被广泛应用的标志存贮服务水平的度量函数，即单位时间的平均缺货额 F_1和平均未偿还的延迟交货额 F_2。

Ensure global convergence of random PSO algorithm for high-dimensional functions is a strong global convergence.

保证全局收敛的随机粒子群优化算法，对于高维函数有较强的全局收敛性。

Stochastic convex programming; Monte Carlo methods; Financial optimization; Convergence with probability one; Optimality condition; Monte Carlo penalty function methods; Nonsmooth optimization; Directional derivative; Subdifferential; Confident interval; Conditional Value-at-Risk; Optimal reinsurance

基础科学，数学，运筹学随机凸规划； Monte Carlo方法；金融优化；以概率1收敛；最优性条件； Monte Carlo罚函数法；非光滑优化；方向导数；次微分；置信区间；条件风险价值；最优再保险

In this paper,the sum of products equality is proved,and the density function of the linear combination of tow-parameters exponential random variable s is presented.

证明了一个关于积和的等式，并由此推导出双参数指数型随机变量的线性组合的概率分布密度函数

The problem has been studied from two sides, firstly, from the viewpoint of applicability, based on the development strategic objectives of the oil company, with the aim to unify the exploration and extraction decisions of the resources in an integrated framework, and integrate the macro economic and technical objectives with micro economic and technical models of an oil well, an integrated non-linear dynamic optimal control model has been constructed, the objective is the benefit maximum of the exploration and extraction of the resources, and the optimalstrategies are obtained by changing the problem into a non-linear mathematical programming problem, on the other hand, from the more macro level, based on the analysis of the characteristics of the exploration and extraction activities of oil and gas resources, a conclusion is easily deduced that the procedure is full of randomicity, then discovering procedure of oil deposit is proved to be a Poisson process, and the reserves process is a supermartingale process, so the model of exploration discovery rate and the reserves model could be constructed.

其次从相对更宏观的层次上，通过对油气资源勘探与开发的特点分析，认为具有很强的随机性，证明了勘探活动发现油气藏的过程为一泊松过程，所发现的油气藏储量为一上鞅过程，在此基础上，建立了油气藏勘探发现率模型及储量模型，在油气价格服从几何布朗运动条件下，以油气开采收益最大化为目标，建立了一个油气资源勘探与开发的随机最优控制模型，采用动态规划方法得到了值函数的HJB方程，并针对方程的特点，以及方程及其变量所对应的经济学意义，对最优策略的求解进行了一些讨论。

Different from traditional system protection models, such as access control matrix model, this theory describes the operations in system by functions of random variable vectors, build an analysis model of trusted system with three axioms, and analyze the information flow in the system by tracing the operation sequence of the system.

与访问控制矩阵模型等传统的保护系统模型不同，这一理论用随机变量向量的函数来描述系统操作，基于三条公设建立了可信系统的分析模型，并通过对系统操作序列的跟踪来分析系统中的信息流。

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。