倒向

In part 3, utilizing the existing Lipschitz results and the property of Yosida approximation of monotone and continuous function, we prove the existence and uniqueness theorem of a general backward stochastic differential equation with monotone and continuous coefficient.

第三部分在系数仅满足单调连续这样一个新条件下，我们综合运用单调连续函数的Yosida逼近的性质以及Lipschitz条件下的已有结果，证明了一般形式的倒向随机微分方程解的存在唯一性。

Under some monotonicity conditions, we give a positive answer to this problem.

在第四章中，我们利用变分方法和对偶技巧最终得到了带时滞正倒向随机控制系统的最大值原理。

In this paper,innovation is:1:We would like to provide a more comprehensive and thorough analysis of the noncallable convertible bonds.

本文的创新点是：1：分析的框架是基于带反射的倒向随机微分方程这个工具。

Our analysis framework relies on the reflected Backward Stochastic Differential equation approach.We characterize the value functions of the noncallable bonds in terms of the reflected Backward Stochastic Differential equation,Then the relationship between the value function of convertible bonds and reflected backward stochastic differential equations with single reflect is built at the same time,and provide the optimal conversion strategy for bondholders.2:We get the value of non-callable convertible bonds by numerical methods.

探讨了可转换债券的最优停时价值与带反射边界倒向随机微分方程解的关系，在市场完备，公司价值只包括股权和可转债这两种权益等各种假定下，给出不可赎回可转换债券的价值函数，证明了不可赎回可转换债券的最优停时问题的解是存在的，同时给出了其最优的转换策略。2：通过数值方法求解不可赎回可转换债券的价值。

We first use the method similar with that in EL.karoui[1] to get the comparison theorem of K in the case of one reflecting barrier,At last,we use the idea of penalization to prove one existence result of the solution for the multi-dimensional RBSDE where the coefficient is continuous and has the linear growth,this also help us to give the comparison theorem of K~+ and K~- in the case of two reflecting barriers.

最后，用惩罚方法证明了当多维双边界反射倒向随机微分方程的生成元满足连续和线形增长条件时解的存在性，并同时得到了双边界情形下，K~+和K~-的多维比较定理。

In chapter Ⅳ, we study forward-backward stochastic differential equations with jumps and with bounded stopping time terminal, which take values in separable Hilbert space, and are drived by cylindrical Brownian motion and Poisson point process.

第四章，研究了取值Hilbert空间的带跳正-倒向随机微分方程，其部分系数不满足李普西茨条件，并且终端时间为有界停时。

The Regis's daughter took a moment to absorb the scene before she collapsed into Scott's slapdash embrace, sighing."I knew you'd return for me, Scott, I knew you'd return."

雷吉斯的女儿吃惊的看着眼前发生的一切，倒向了斯科特仓促的拥抱，叹息着："我知道你会回来找我的，斯科特，我知道你会回来。"

In Chapter 3, the existence and uniqueness of time-delayed forward-backward stochastic differential equation are considered.

在第三章中，我们研究了带时滞的正倒向随机微分方程解的存在唯一性问题，在一定的单调性假设条件下，我们对这一问题给出了肯定的回答。

For example, in mathematical finance, options, as one of financial derivatives, its price can be solved by a backward stochastic differential equation.

比如， 在金融领域，作为金融衍生工具之一的期权，它的理论价格可以用倒向随机微分方程解出。

Moreover, applying the theories of backward stochastic differential equation and partial differential equation, the models have been converted.

并借助于倒向随机微分方程以及偏微分方程的重要理论完成了对模型的转化。

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。