本文選題：多值倒向隨機(jī)微分方程 + G-布朗運(yùn)動(dòng)�。� 參考：《安徽師范大學(xué)》2017年碩士論文

【摘要】：本論文主要研究由G布朗運(yùn)動(dòng)驅(qū)動(dòng)的多值倒向隨機(jī)微分方程及其大偏差.全文共分為三個(gè)部分.首先,我們通過Moreau-Yosida逼近法證明如下由G布朗運(yùn)動(dòng)驅(qū)動(dòng)的倒向隨機(jī)微分方程解的存在唯一性:其中B.為G-布朗運(yùn)動(dòng),B.為B.對(duì)應(yīng)的二次變差過程,(?)φ為φ對(duì)應(yīng)的次微分算子,其為Rd上的下半連續(xù)函數(shù).進(jìn)一步,我們考慮如下由G-布朗運(yùn)動(dòng)驅(qū)動(dòng)的多值耦合的正-倒向隨機(jī)微分方程其中定義:u(t,x)=Y_t~(t,x).我們得到了其為下述非線性變分不等式的粘性解:其次,我們建立了由G-布朗運(yùn)動(dòng)驅(qū)動(dòng)的隨機(jī)微分方程的大偏差.為此,我們考慮如下由G-布朗運(yùn)動(dòng)驅(qū)動(dòng)的耦合正-倒向隨機(jī)微分方程證明了方程的解(Xx,∈,Yx,∈,Zx ∈)收斂到如下的確定性方程的解(Xx,Yx,Zx),并且建立了Yx,∈t, 滿足的大偏差原理.最后,我們研究了由G-布朗運(yùn)動(dòng)驅(qū)動(dòng)的多值倒向隨機(jī)微分方程的大偏差問題.為此,我們考慮如下由G-布朗運(yùn)動(dòng)驅(qū)動(dòng)的多值耦合正-倒向隨機(jī)微分方程我們證明了上述方程的解收斂到如下系統(tǒng)并給出了解所滿足的大偏差原理.
[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.
【學(xué)位授予單位】：安徽師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O211.63
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本文編號(hào)：2086837