精品文档---下载后可任意编辑倒向随机微分方程下的算子表示及 Jensen 不等式的开题报告开题报告题目：倒向随机微分方程下的算子表示及 Jensen 不等式摘要：本文讨论了倒向随机微分方程下的算子表示及 Jensen 不等式。在此基础上，运用随机积分理论，得到了该类方程的算子表示，并证明了 Jensen 不等式在该类方程中的适用性。具体而言，本文将首先介绍倒向随机微分方程及其解的定义，接着引入了算子表示的概念，并详细讨论了如何利用算子表示来表达解析函数。随后，本文将探讨倒向随机微分方程中的随机积分，定义 Martingale 型随机积分的等价关系并证明了其性质，利用 Martingale 型随机积分的理论，本文得到了倒向随机微分方程的算子表示。最后，本文将给出 Jensen 不等式的定义，并证明在倒向随机微分方程中其仍然适用。关键词：倒向随机微分方程；算子表示；随机积分；Martingale 型随机积分；Jensen 不等式Abstract: This paper studies the operator representation and Jensen's inequality under the backward stochastic differential equation. Based on the stochastic integral theory, the operator representation of this type of equation is obtained, and the applicability of Jensen's inequality in this type of equation is proved. Specifically, this paper will first introduce the definition of backward stochastic differential equations and their solutions, and then introduce the concept of operator representation, and discuss in detail how to use operator representation to express analytic functions. Subsequently, this paper will explore stochastic integration in backward stochastic differential equations, define the equivalence relation of Martingale-type stochastic integration and prove its properties. Based on the theory of Martingale-type stochastic integration, this paper obtains the operator representation of backward stochastic differential equations. Finally, this paper will give the definition of Jensen's inequality and prove that it is still applicable in backward stochastic differential equations.精品文档---下载后可任意编辑Keywords: backward stochastic differential equations; operator representation; stochastic integration; Martingale-type stochastic integration; Jensen's inequality
