复不确定微分方程解的存在唯一性

发布时间：2018-03-17 07:46

本文选题：不确定变量　切入点：不确定过程　出处：《河北大学》2017年硕士论文　论文类型：学位论文

【摘要】：自然界中存在着各种各样的不确定现象,随着时代的发展与科技的进步,现实生活中的不确定现象也越来越多,概率论和模糊理论不能解决的问题也随之增加.为了更好地处理不确定现象,产生了不确定理论.不确定理论是一种新的处理人的主观不确定性的公理化体系方法.在不确定理论的框架下,本文通过对强同单调不确定过程进行研究,得出了关于强同单调不确定过程及其积分的一些性质.通过对复不确定过程及其分布函数的研究,得出了不确定积分与复不确定积分的一些性质.最后,对复不确定微分方程的求解方法进行研究,得出了复不确定微分方程解的存在唯一性定理.本文的主要内容有:1.定义并讨论了强同单调不确定过程的加法和数乘性质以及关于强同单调不确定过程积分的非负性、单调性和几个积分不等式.2.引入了复不确定过程分布函数的概念,给出了复不确定过程分布的一个充要条件,研究了复不确定过程的独立性、期望和方差等,讨论了不确定积分与复不确定积分的存在性问题,同时研究了其它不确定积分的一些基本性质.3.探讨了复不确定微分方程的解并证明了复不确定微分方程解的存在唯一性定理.
[Abstract]:There are various kinds of uncertainties in nature. With the development of the times and the progress of science and technology, there are more and more uncertainties in real life. The number of problems that cannot be solved by probability theory and fuzzy theory increases. In order to better deal with uncertainties, Uncertainty theory is a new axiomatic system method to deal with human's subjective uncertainty. Under the framework of uncertainty theory, this paper studies the strongly isomorphic monotone uncertain process. Some properties of strongly isomorphic monotone uncertain processes and their integrals are obtained. By studying complex uncertain processes and their distribution functions, some properties of uncertain integrals and complex uncertain integrals are obtained. The method of solving complex uncertain differential equations is studied. The existence and uniqueness theorems of solutions for complex uncertain differential equations are obtained. The main contents of this paper are: 1.Defining and discussing the additive and multiplicative properties of strongly identical monotone uncertain processes and the nonnegativity of integrals for strongly isomorphic uncertain processes. The concept of distribution function of complex uncertain processes is introduced, a sufficient and necessary condition for the distribution of complex uncertain processes is given, and the independence, expectation and variance of complex uncertain processes are studied. This paper discusses the existence of uncertain integrals and complex uncertain integrals, studies some basic properties of other uncertain integrals, discusses the solutions of complex uncertain differential equations and proves the existence and uniqueness theorems of solutions of complex uncertain differential equations.
【学位授予单位】：河北大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

【参考文献】