鞅

Theorem 2 gives the sufficient and necessary condition of continuous parameter set-valued submartingale existing Doob-Meyer decomposition.

定理 2给出了连续参数集值下鞅存在唯一的Doob Meyer分解的充要条件

The almost sure convergence properties of general Jamison weighted sums of submartingale difference random sequence sis was discussed.

通过讨论下鞅差序列的广义 Jamison型加权和的几乎处处收敛性，获得了比独立情形还强的 Jamison定理和 Marcinkiewicz强大数律，推广和改进了这两个定

A government monopolizing land leads to the submartingale of expected house price if it holds short-term target, which would increase the speculating demand of house.

垄断土地所有权的政府如果具有短期政绩目标函数，他们对土地的控制会使房地产预期价格具有不断上涨的下鞅性，这会提高住房的投机性需求。

The convergence with discrete parameter of set-valued supermartingale had been investigated by many scholars.

离散参数集值上鞅的收敛性已有诸多学者研究过。

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。

In order to get the convergence properties of the weak set-valued Amart , we firstly proved the theorem that the limit of support functions is a support function.

为了得到关于弱集值渐近鞅的收敛性质，首先证明了支撑函数列的极限亦为一支撑函数。

This paper,uses the property of being uniformly integrable to truncate the random variable sequences,and under the condition of φx↑,φx2↓,obtain a weak law of large number of martingale difference sequences by the weak convergence theorem.

通过使用一致收敛性对随机变量序列进行截尾，并借助随机变量序列的弱收敛定理，在φ↑，φx2↓的条件下给出了一个鞅差序列的弱大数定律。

With the help of mildconditions,Burkholder-Davis-Gundy\'s inequality and Doob\'s inequality of tree mar-tingales are proved by the application of this method.

在合理假设下，用这种方法证明了树鞅的Burkholder-Davis-Gundy\'s不等式及Doob不等式。

By using truncation methods of random variables and Doob martingale convergence theorem,the properties of sequence of arbitrary random variables are studied,a class of strong limit theorems for sequences of arbitrary random variables is obtained under moment conditions, and some conclusions corresponded to these are generalized.

利用随机变量的截尾方法和Doob鞅收敛定理，研究了任意随机变量序列的性质，得到了一类矩条件下任意随机变量序列的强极限定理，推广了与此相应的一些结果

Chapter 3 discusses the fundamentals inequalities in the rearrangement invariant martingale space, such as the corresponding important Doob"s maximal inequality, Burkholder-Gundy-Davis inequality and Rosenthal"s inequality.

第三章讨论重排不变鞅空间中的基本不等式，包括Doob极大不等式、Burkholder-Gundy-Davis不等式和Rosenthal不等式。

And Pharaoh spoke to Joseph, saying, Your father and your brothers have come to you.

47：5 法老对约瑟说，你父亲和你弟兄们到你这里来了。

Additionally, the approximate flattening of surface strip using lines linking midpoints on perpendicular lines between geodesic curves and the unconditional extreme value method are discussed.

提出了用测地线方程、曲面上两点间短程线来计算膜结构曲面测地线的方法，同时，采用测地线间垂线的中点连线和用无约束极值法进行空间条状曲面近似展开的分析。