鞅

Firstly, we consider the problem of the representation formula for the transition probability density of a right process under Girsanov transform. Secondly,we consider the problem of the MEMMs (minimal entropy martingale measure)for Markov switching Levy processes, and justify that the minimal entropy martingale measure is obtained by some regime switching Esscher transform. At last,we consider the problem of the invariant measure and the ergodic property of recurrent right processes. This paper includes 5 chapters.

首先，我们考虑了满足一定条件的右过程在Girsanov变换下的转移概率密度的表达式问题；其次，我们考虑了由Markov调制的Lévy过程的最小相对熵鞅测度的问题，证明了其最小相对熵鞅测度是某个状态转换Esscher变换；最后，我们考虑了右过程的不变测度及其遍历性的问题。

This thesis is devoted to the consideration and study of martingale space and inequality theory in the background of a rearrangement invariant function space on finite interval.

本文系统地考虑和研究了有限区间上重排不变函数空间框架下的鞅不等式和鞅空间。

Using martingale methods, and choosing the stock as numeraire asset and corresponding equivalent martingale measure, the author gets the simple pricing formula by the Asian option in the case of geometric average.

主要研究了股票价格过程由几何Lévy过程驱动的亚式期权的定价问题，利用鞅方法，选择股票作为计价单位及相应的等价鞅测度给出了几何平均亚式期权简单的定价公式。

New properties and improvements on VSI. Combining the density processof local absolute continuous measure, properties of the martingale space H1 and semi-martingale space, and the closed image theorem of functional analysis (see the proofs ofTheorem 2.4.5 and Theorem 2.4.10), we obtain the general form of Girsanov Theorem forsemi-martingale vector stochastic integral .

特别是利用局部绝对连续测度的密度过程、鞅空间H1与半鞅空间的性质以及泛函分析中的闭图像定理(见定理2.4.5与定理2.4.10的证明)获得了一般形式的半鞅向(来源：Ab6BC论a1文网www.abclunwen.com)量随机积分的Girsa-nov定理，它对于随机分析的理论与随机积分的应用都具有重要价值。

In this paper, with the Doob decomposition of B-valued uniform amart s.

B值一致渐近鞅是B值鞅的重要推广，它保持了鞅的一些最基本的性质。

With Doob decomposition of B-valued asymptotic martingale , studies the law of large numbers of B-valued asymptotic martingale , some results are obtained.

利用B值渐近鞅的Doob分解定理，研究了B值渐近鞅的大数定律，它们是鞅的有关结论的推广和改进。

And these results not only extend the classical inequalities of martingale Hardy space, but also point out the close affiliation between the Boyd indices of rearrangement invariant martingale space and the characters of the martingales in it.

这些结果不仅推广了经典鞅Hardy空间中的不等式，而且深刻地揭示了重排不变鞅空间的Boyd指数和其中鞅性质的密切联系。

Based on the tree martingale decomposition theorem and the con-vergence of locally finite tree martingales,a tree martingale convergence theorem isverified.

再基于树鞅分解定理和局部有限树鞅收敛定理，证明了一个树鞅收敛定理。

In Chapter 7,we study martingales with respect to a Clifford algebra valuedmeasure,get the equivalence of some kinds of Clifford martingale spaces and prove theseClifford martingale spaces are isomorphic to the spaces of martingales with respect tothe corresponding real measure.

第七章研究一类特殊的Clifford代数值鞅，建立了几种Clifford鞅空间之间的等价性，并且证明它们与相应的实测度鞅空间同构。

On this basis,thelocally finite tree set is defined,and the locally finite tree martingales are defined interms of the locally finite tree set,and then a tree martingale decomposition theoremis obtained by the locally finite tree martingales.

在这个结果的基础上，我们定义了局部有限树集的概念，利用这个概念又定义了局部有限树鞅，通过局部有限树鞅给出了树鞅分解定理。

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。