由G布朗运动驱动的多值倒向随机微分方程

发布时间：2018-06-30 21:01

  本文选题：多值倒向随机微分方程 + G-布朗运动　； 参考：《安徽师范大学》2017年硕士论文

【摘要】：本论文主要研究由G布朗运动驱动的多值倒向随机微分方程及其大偏差.全文共分为三个部分.首先,我们通过Moreau-Yosida逼近法证明如下由G布朗运动驱动的倒向随机微分方程解的存在唯一性:其中B.为G-布朗运动,B.为B.对应的二次变差过程,(?)φ为φ对应的次微分算子,其为Rd上的下半连续函数.进一步,我们考虑如下由G-布朗运动驱动的多值耦合的正-倒向随机微分方程其中定义:u(t,x)=Y_t~(t,x).我们得到了其为下述非线性变分不等式的粘性解:其次,我们建立了由G-布朗运动驱动的随机微分方程的大偏差.为此,我们考虑如下由G-布朗运动驱动的耦合正-倒向随机微分方程证明了方程的解(Xx,∈,Yx,∈,Zx ∈)收敛到如下的确定性方程的解(Xx,Yx,Zx),并且建立了Yx,∈t, 满足的大偏差原理.最后,我们研究了由G-布朗运动驱动的多值倒向随机微分方程的大偏差问题.为此,我们考虑如下由G-布朗运动驱动的多值耦合正-倒向随机微分方程我们证明了上述方程的解收敛到如下系统并给出了解所满足的大偏差原理.
[Abstract]:In this paper, we mainly study the multivalued backward stochastic differential equations driven by G Brown motion and their large deviations. The full text is divided into three parts. First, we prove the existence and uniqueness of the solution of the backward stochastic differential equation driven by the G Brown motion by the Moreau-Yosida approximation method: B. is G- Brown motion and B. is the corresponding variation of B.. The process, (?) is the sub differential operator of the corresponding Rd, and it is the lower semi continuous function on Rd. Further, we consider the following definition of the positive backward stochastic differential equation which is driven by the G- Brown motion. We have obtained the viscous solutions of the following nonlinear variational inequalities. Secondly, we have established the G- Brown. The large deviation of the motion driven stochastic differential equation. For this, we consider the following coupled positive backward stochastic differential equations driven by G- Brown motion to prove that the solution of the equation (Xx, Yx, Zx, Zx) converges to the solution of the deterministic equation (Xx, Yx, Zx), and establishes a Yx, a T, a large deviation principle. Finally, we study the G The large deviation problem of a multi value backward stochastic differential equation driven by Brown motion is considered. For this reason, we consider the multivalue coupled forward backward stochastic differential equation driven by the G- Brown motion. We prove that the solution of the above equation converges to the following system and gives the large deviation principle of understanding.
【学位授予单位】：安徽师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.63
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本文编号：2086837