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Chapter 1 gives the background,current research process of relatedproblems and summarizes this thesis\'s work.In chapter 2,we study the Brownian motion with holding and jumping on the boundary.We use the resolvent method to obtain the infinitesimal generator because the domain of the infinitesimal generator is essentially the same as the range of the resolvent.Knowledge of this range and of the differential operator determines uniquely the infinitesimal generator.Since the semigroup generated by the DHJ is not strongly continuous,to use the nice property of strongly continuous semigroup in analytic theory,in chapter 3 we show that the dual is strongly continuous and derive ergodicity through spectral radius formulas and finally obtain the ergodic theorem by duality. In chapter 4,we discuss a class of a more general process---one dimensional Feller diffusion proposed by W.Feller in 1954.The Feller diffusion allows the possibility of jumps from boundary to boundary,not only from boundary to the interior.We give the stationary distribution of this process.

具体地，本文的结构如下：第一章给出了问题产生的背景，研究现状及本文的主要工作；第二章研究了在边界上逗留后随机跳的布朗运动，我(来源：3dABC论文网www.abclunwen.com)们用预解算子的方法得到其无穷小生成元，因为无穷小生成元的定义域本质上就是预解算子的值域，知道这个值域和微分算子形式就能唯一地决定无穷小生成元；由于DHJ过程产生的半群不是强连续的，为利用强连续半群的一些漂亮性质，在第三章中我们证明其对偶半群是强连续的，然后由谱半径公式得到遍历性并且最后由对偶得到遍历定理；第四章讨论了Feller在1954年引入的更广的一类过程----一维Feller扩散过程，Feller扩散过程允许有从边界到边界的跳发生，即不仅仅局限于从边界到内部的跳，在这一章中，我们给出了一维Feller扩散过程的平稳分布；在第五章，我们讨论了一些相关的问题，给出了DHJ过程对应的PDE问题及特征值与收敛速度的关系。

Traditional security is embodied in national egocentrism , essentially based on whether it helps or is detrimental to the national interests , sovereignty and territorial safety , with good and evil as the fundamental criterion of moral judgment .

传统安全实质上体现的是一种国家中心主义的伦理向度，非传统安全则主要体现的是全球中心主义的伦理向度。

Device for converting sound waves into electric power that has wave characteristics essentially similar to those of the sound.

将声波转换成电功率并保持其波形特性基本相似的装置。

Essentially, an induction lamp is an electrodeless fluorescent.

无极灯没有电极，依靠电磁感应和气体放电的基本原理而发光。

The shape of these layers is irregular but essentially ellipsoidal.

这些地层的形状并不规则，虽然近似地接近一个椭球。

What makes Active Server Pages convenient is the fact that they are essentially HTML pages with embedded ASP code.

最令活跃服务器页方便的是，他们基本上协议文本嵌入代码页。

He says, it is to embezzle essentially the network access of others, and by pilfer person network access is bought, have exclusive sex.

他说，实质上是盗用别人的网络使用权，而被盗者的网络使用权是买来的，具有独占性。

If this is the case with your employer, there is essentially nothing that you can do about it.

如果是这样的话你的雇主，你有什么实质上都没有。

Why would you want to leave an established career at your present employer for an essentially entry-level position?

为什么你要离开一个既定的职业生涯，你现在的雇主基本上属于入门级的地位呢？

This was essentially a policy of equalization of land use, reminiscent of traditional reform efforts.

这根本上是土地利用的平衡政策，回忆传统改革努力。

The United Kingdom has pledged to provide technical assistance to the peacekeeping effort in Darfur, including airlifting supplies and equipment to assist the African peacekeepers.

英国承诺为达佛的維和努力提供技术帮助，包括提供非洲的維和部队空运补給和裝备。

Results: The level of ET-1mRNA in placental villus was significantly higher in pre-eclamptic women than that in control group.

结果：妊高征组患者胎盘绒毛组织ET-1 mRNA的表达较正常妊娠组明显增高。