随机微分方程

词组短语

stochastic differential equation

与随机微分方程相关的网络例句 [注：此内容来源于网络，仅供参考]

Relative to SDE, the study for the solution of BSDE under non-Lipschitz condition is absence, especially when the uniqueness of the solution can not be guaranteed, the existence of minimal and maximal solution of BSDE are not be studied.

相对于正向随机微分方程，非Lipschitz条件下倒向随机微分方程解的性质的研究尚不够丰富，特别是条件不能保证方程解唯一时，倒向随机微分方程最大最小解的存在性尚未见有成果。

In chapter two, under non-Lipschitz condition, the existence and uniqueness of the solution of the second kind of BSDE is researched, based on it, the stability of the solution is proved; In chapter three, under non-Lipschitz condition, the comparison theorem of the solution of the second kind of BSDE is proved and using the monotone iterative technique , the existence of minimal and maximal solution is constructively proved; in chapter four, on the base of above results, we get some results of the second kind of BSDE which partly decouple with SDE, which include that the solution of the BSDE is continuous in the initial value of SDE and the application to optimal control and dynamic programming. At the end of this section, the character of the corresponding utility function has been discussed, e.g monotonicity, concavity and risk aversion; in chapter 5, for the first land of BSDE ,using the monotone iterative technique , the existence of minimal and maximal solution is proved and other characters and applications to utility function are studied.

首先，第二章在非Lipschitz条件下，研究了第二类方程的解的存在唯一性问题，在此基础上，又证明了解的稳定性；第三章在非Lipschitz条件下，证明了第二类BSDE解的比较定理，并在此基础上，利用单调迭代的方法，构造性证明了最大、最小解的存在性；第四章在以上的一些理论基础之上，得到了相应的与第二类倒向随机微分方程耦合的正倒向随机微分方程系统的一些结果，主要包括倒向随机微分方程的解关于正向随机微分方程的初值是具有连续性的，得到了最优控制和动态规划的一些结果，在这一章的最后还讨论了相应的效用函数的性质，如，效用函数的单调性、凹性以及风险规避性等；第五章，针对第一类倒向随机微分方程，运用单调迭代方法，证明了最大和最小解的存在性，并研究了解的其它性质及在效用函数上的应用。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utility function are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

This paper study the character and application of the solution of BSDE, the main results include: for the second kind of BSDE, the existence and uniqueness of the solution under non-Lipschitz condition, comparison theorem and stability are established , under weaker condition , the existence of the minimal and maximal solution is proved and the application in stochastic control and utility function is given; for the first kind of BSDE, under weaker condition , the existence of minimal and maximal solution .stability, comparison theorem and application to utilityfunction are proved.

本文研究倒向随机微分方程解的性质及其应用，主要结果有：针对第二类方程，讨论了在非Lipschitz条件下倒向随机微分方程解的存在唯一性，比较定理及稳定性等，在更弱条件下，得到了倒向随机微分方程的最大解和最小解的存在性，在此基础之上，给出了在随机控制及效用函数方面的应用；针对第一类方程，同样在较弱条件下，证明了方程最大、最小解的存在性、稳定性、比较定理及其在效用函数的应用。

Then the explicit expression of it under exponential claims and the differential equation are obtained.Thus we discuss the effects of credit and debit interests on it through data analysis. Through the research of the mean,the moment generating function and the higher moments of discounted aggregate dividend payments,we discuss the optimal dividend payments problems.

而对于Gerber-Shiu函数的研究，则是通过随机过程及随机微分方程的知识得到它满足的积分-微分方程及边值问题，然后得到了它在指数索赔下的明确表达式以及Erlang(2)索赔下满足的微分方程，并通过数值分析得到贷款利息及存款利息对它的影响。

Differential equation model is classified as ordinary differential equation, partial differential equation and stochastic differential equation.

微分方程模型的形式包括常微分方程，偏微分方程和随机微分方程。

This leads to a parabolic partial differential equation for price of bond.

假设利率变化的模型是由随机微分方程给出的，则可以用推倒Black－Scholes方程的方法来推出债券价格满足的偏微分方程，得到一个抛物型的偏微分方程。

By introducing random factors on differential equation, stochastic differential equation is formed.

微分方程反映了系统中的动态变化情况，在实际生产生活中得到了广泛的应用；微分方程的基础上引入随机因素，便形成了随机微分方程。

Therefore, basic methodologies for stochastic seismic and filtering responses of nonlinear structure are studied, the approximate solution methodologies and their practical applications are investigated in the dissertation employing equivalent linearization and moment equations method based on FPK equations and Ito stochastic differential equations. The research works are mainly concerned with the following aspects:Firstly, the differential expression of bilinear hysteretic is studied and a new differential expression is developed, then they are demonstrated.

因此，本文基于FPK方程和伊藤随机微分方程，研究了滞后结构物的随机地震反应和随机滤波问题的基本方法，并利用等效线性化法和矩方程法，研究了非线性结构随机地震反应分析和随机滤波分析的近似解法及它们的工程应用。

An example of these maximal monotone operators is the subdifferential of a closed convex function.

这种多值极大单调算子的一个特殊例子是闭凸函数的下微分算子，所以本文考虑的多值随机微分方程包含了在凸区域内具有反射边界的随机微分方程。

与随机微分方程相关的网络解释 [注：此内容来源于网络，仅供参考]

stochastic functional equation：随机函数方程

随机微分方程 stochastic differential equation | 随机函数方程 stochastic functional equation | 随机独立 stochastic independence

stochastic differential equation：随机微分方程

他于1944年和 1946年的两份著作建立随机积分( stochastic calculus )和随机微分方程(stochastic differential equation)的理论基础,被认为是随机分析的开创者.

backward stochastic differential equation：倒向随机微分方程

高阶中立型微分方程:high order neutral differential equation | 倒向随机微分方程:backward stochastic differential equation | (正)倒向随机微分方程:(Forward) Backward Stochastic Differential Equation

stochastic differential equation, SDE：随机微分方程

随机完全区组设计|randomized complete-block design | 随机微分方程|stochastic differential equation, SDE | 随机微分方程[的]强解|strong solution of SDE

(Forward) Backward Stochastic Differential Equation：(正)倒向随机微分方程

倒向随机微分方程:backward stochastic differential equatio... | (正)倒向随机微分方程:(Forward) Backward Stochastic Differential Equation | 倒向随机微分方程:Backward Stochastic Differential Equation (BSD...

Backward Stochastic Differential Equation (BSDE)：倒向随机微分方程

(正)倒向随机微分方程:(Forward) Backward Stochastic... | 倒向随机微分方程:Backward Stochastic Differential Equation (BSDE) | 微分方程的等效积分对称弱形式:symmetric weak form of the equivalent integral e...

stochastic differentiation：随机微分法

stochastic differential equation 随机微分方程 | stochastic differentiation 随机微分法 | stochastic dynamic model 随机动态模型

stochastic differentiation：随机微分

stochastic differential equation 随机微分方程 | stochastic differentiation 随机微分 | stochastic integral 随机积分

strong solution of SDE：随机微分方程[的]强解

随机微分方程|stochastic differential equation, SDE | 随机微分方程[的]强解|strong solution of SDE | 随机微分方程[的]弱解|weak solution of SDE

weak solution of SDE：随机微分方程[的]弱解

随机微分方程[的]强解|strong solution of SDE | 随机微分方程[的]弱解|weak solution of SDE | 随机微分几何|stochastic differential geometry