鞅

It was proved that under Lipschitz coefficients, the solutions of SDEs driven by Brownian motion or a continuous semimartingale form a stochastic homeomorphism flow.

在方程系数Lipschitz连续的条件下，由Brown运动或连续半鞅驱动的随机微分方程的解形成一随机同胚流。

Because of the incompletion in real option theory, this paper studies the effect of market certainty and uncertainty on project investing decision were studied by using martingale theory.

针对实物期权理论中存在的不足，运用鞅理论分析研究了市场环境下的确定性和不确定性因素对实物资产项目投资决策的影响。

Chapter 1 we introduce the risk process with positive and negative risk sums,show the background of the risk process. Chapter 2 we show the integral and differential equation of birth probability,give the Lundberg inequation that the ruin probability satisfies with martingale approach,then discuss then ruin probability of the risk process with two dependent positive and negative risk sums,study how the dependence impacts on the ruin probability. Chapter 3 we compare the concrete examples by numbers,and makes further comparison between the two results coming out of independency and dependency,with the purpose of narrating their respective impacts on the probability of ruin probability.

本文第一章引入含正、负风险和的风险模型，介绍风险过程的实际背景；第二章给出生存概率Φ所满足的积分-微分方程，利用典型鞅方法给出破产概率Ψ满足的Lundberg不等式，并且讨论两个相关正、负风险和模型的破产概率，研究相关性对破产概率的影响；第三章对具体实例给出数值比较，进一步把相关性和独立性两种情形的结果进行比较，说明对破产概率的影响。

Convergence supper martingal and analytical method, a strong limit theorem for Laplace distribution is obtained.

利用似然比构造几乎处处收敛的上鞅，结合分析方法，给出了 Laplace分布的一个强极限定理。

Finally the connections between the Lebesgue measure for its image and Bessel-Ricsz capacity are discussed and an explicit Bessel-Riesz capacity estimate is obtained.

利用鞅的方法讨论了广义布朗单的碰撞概率与容度之间的关系，给出了其碰撞概率的容度估计。

Shangjunshu is an important document of Legalist School, reflected the main ideas of Shang Yang and his school. It had played a decisive role in the formation and development of the absolute monarchy system which had been lasting for more than 2,000 years, so, it is of a higher literature value and ideological value.

商君书》是法家的重要文献，反映了商鞅及其学派的主要思想，曾对延续二千馀年的君主专制体制的形成和发展起过决定性的作用，所以有较高的文献价值和思想价值，有必要从这两方面进行研究。

What he advocated was, what I may call, the "limited version" of the Monarchy system of the United Kingdom.

我对商鞅法治的最为敬佩之处，就在于它的法治思想远远超越他的时代。

As an alternative,we turned back to find the limiting distribution of the LSS G_n.

本文主要运用Bernstein多项式逼近、Stieltjes变换方法以及鞅的中心极限定理等手法。

The logion rule by law was first brought forward by Guan Zi and we still say it today.

战国时期，各国开始变法改革，秦国的商鞅改革最为成功。

That's why martingale systems don't work.

这就是为什么鞅系统不工作。

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。