随机微分方程均方有界解存在性判定的研究.docxVIP

PAGE PAGE II 毕业论文 题 目 随机微分方程均方有界解存在性判定的研究 学 院 专业班级 学 号 姓 名 指导教师 二〇一七年六月九日 PAGE PAGE I 中 文 摘 要 随机微分方程被广泛的应用在许多领域，如在经济学中，自然科学中，工程技术中，人口生态学中等众多领域。事实上，使用随机微分方程来建模可以更真实，更准确的刻画系统的运行状态。其中，解的稳定性是指解在时间进程中具有什么极限状态，以及极限状态如何依赖于初始值。稳定性在系统分析及微分方程的定性理论研究中处于十分重要的地位，一直是人们研究方程的重点与热点。因此研究随机微分方程解稳定性是一项非常有意义的工作。 本文第一章介绍了本文工作的背景以及本文的结构及主要工作；第二章作为准备知识给出了本文要用到的相关内容，其中包括随机微分方程的基本概念和论文中要用到的基本定理；第三章展示了本文的主要结果，对在随机微分方程的系数满足全局Lipschitz条件，取值于欧氏空间中某个紧集时，我们可以根据方程的一个在半实轴上呈现出均方有界性的解推出，方程具有在全空间上均方有界性的解。进行了证明，从而证明了是一个有界解；第四章给出了结论。 关键词 随机微分方程 布朗运动 随机过程 鞅 解的唯一性 有界性 PAGE PAGE II Title A study on the existence of mean square bounded solution of stochastic differential equations Abstract Stochastic differential equations are widely used in many fields, such as in economics, in natural science, in engineering, and in many areas of population ecology. In fact, the use of stochastic differential equations to model can be more realistic and more accurate description of the systems operating state. The stability of the solution refers to the limit state of the solution in the time process, and how the limit state depends on the initial value. Stability plays an important role in system analysis and qualitative theory of differential equations. It has been the focus and hot spot for people to study equations. Therefore, it is a very meaningful job to study the stability of stochastic differential equations. The first chapter introduces the background of the work and structure of this article and the main work; the second chapter is the related content to give knowledge will be used in this paper, the basic concept and the basic theorem including stochastic differential equations will be used; The third chapter shows the main results of this paper, the coefficient on the stochastic differential equation to satisfy global Lipschitz conditions, valued in Euclidean space in a compact set, we can according to the equation in a real half axis shows the mean square boundedness