倒向

The solution of a backward stochastic differential equation is a pair of process satisfyingwhere g is the generator, and ξ is the terminal condition.

倒向随机微分方程的解是一对过程满足其中g是生成子，ζ是终端条件。

Firstly, we prove the existence and uniqueness of the adapted solution of multi-dimensional backward stochastic differential equations driven by Brownian motion and Lévy process by using predictable representation theorem and the fixed point theorem about contract mapping, and also prove the comparison theory.

第一部分运用可料表示定理和压缩映射原理证明由布朗运动和Lévy过程共同驱动的多维倒向随机微分方程适应解的存在唯一性及其相应的比较定理。

Huang and Lin proposed the weak solution concept for Backward Stochastic Differential Equation This paper based on the predecessor's work , gives the weak solution concept for Backward Stochastic Differential Equation with continuous martingale,uses the Girsanov transformation, obtains its weak solution of the existence of a necessary and sufficient conditions, and on this basis obtains its weak solution of the existence of sufficient conditions,these sufficient conditions weakened the drifting coefficient which requested in the existence uniqueness of strong solution to satisfy the Lipschitz condition the request.

本文在前人研究的基础上，给出由连续鞅驱动的倒向随机微分方程弱解的概念，利用Girsanov变换，得到其弱解存在的存在的一个充分必要条件，并在此基础上得到了其弱解存在的一些充分条件，这些充分条件减弱了在强解的存在唯一性中要求的漂移系数满足Lipschitz条件的要求。

Secondly, we consider stochastic LQ optimal control problem driven by Lévy processes and Brownian motion. By applying the -Lévy formula, Gronwall's inequality, Young's inequality and Cauchy-Schwarz inequality, we obtain the closeness property of the solution of multi-dimensional backward stochastic Riccati differential equations.

第二部分首先研究由布朗运动和Lévy过程共同驱动的随机LQ最优控制问题，接着利用-Lévy公式、Gronwall不等式、Young不等式及Cauchy-Schwarz不等式证明多维倒向随机Riccati微分方程适应解的闭性质，并利用此性质证明一维BSRDE解的存在唯一性。

We are not talking of surrendering to the bourgeoise democracy. This is not at all connected with that.

我们不是说倒向资产阶级民主，这与那毫无关系。

In part 1, we explore some properties of solution y of a backward stochastic differential equation, such as comparison theorem, reverse comparison theorem and uniqueness theorem of generator.

第一部分研究了倒向随机微分方程的解中y的性质，其中包括解的比较定理，逆比较定理，生成元的唯一性定理。

Under the most elementary conditions for backward stochastic differential equation introduced by Peng S., we put forward and prove a general converse comparison theorem.

在由彭实戈引入的倒向随机微分方程的最基本的条件下，提出并证明了一个一般的反比较定理。

In this paper, we study the comparison theorem of backward doubly stochastic differ-ential equtions with continuous coefficient by Tanaka-Meyer formula.

利用Tanaka-Meyer公式研究了双重倒向随机微分方程在连续条件下的比较定理。

In this article, we discuss the solution ofbackward stochastic differential equation and the generalizes comparison theorem and concernedthe relation between g-Expection and the minimum expection.

本文主要讨论如上倒向随机微分方程的解的情况及相应的g-期望的性质以及其在数学金融方面的应用。

In this paper, we consider the optimal control problem of time-delayed forward-backward stochastic system when control set is convex.

本文研究了在控制集为凸集的情况下带时滞的正倒向随机控制系统的最优控制问题。

He is the most remarkable man that I have ever known.

他是我知道的人中最值得注意的人。

Increased appearance of lymphocele was noticed in patients with diabetic nephropathy, congenital malformations of the urinary tract, and inflammatory diseases, including glomerulopathy and extraglomerular ones, after high-voltage radiotherapy and after removal of the renal graft.

经过高压放射疗法和切除移植肾后，在糖尿病肾病患者、泌尿系统先天性畸形患者和炎症患者身上发现淋巴囊肿有所增加，包括肾小球病和球外疾病等。