SMALLEST g-SUPERSOLUTION FOR BSDE WITH CONTINUOUS DRIFT COEFFICIENTS

91. IntroductionSince the result of monotonic lied theorem of BSDE and its aPPlication to nonlinearDoolyMeyer decomposition theorem, the smallest g-supersolution with a constraint on (Y, Z)(see [1]), some developments have been done, for example, in 14], where by a penallzationmethod, Chen and Peng discussed nonlinear Doob-Meyer decomposition theorem ash theBSDE introduced by Duffie and EPsteinI3]. In [51 Lin discussed the smallest g-supersolutionto BSDE with a constraint on (y,z) wi…     

高维倒向随机微分方程比较定理

倒向随机微分方程由Pardoux和彭实戈首先提出，彭实戈给出了一维BSDE的比较定理，周海滨将其推广到了高维情形．毛学荣将倒向随机微分方程解的存在唯一性定理推广到非Lipschitz系数情况，曹志刚和严加安给了相应的一维比较定理．本文将曹志刚和严加安的比较定理推广到高维情形．     

BSDEs and SDEs with time-advanced and -delayed coefficients

ABSTRACT

This paper introduces a class of backward stochastic differential equations (BSDEs), whose coefficients not only depend on the value of its solutions of the present but also the past and the future. For a sufficiently small time delay or a sufficiently small Lipschitz constant, the existence and uniqueness of such BSDEs is obtained. As an adjoint process, a class of stochastic differential equations (SDEs) is introduced, whose coefficients also depend on the present, the past and the future of its solutions. The existence and uniqueness of such SDEs is proved for a sufficiently small time advance or a sufficiently small Lipschitz constant. A duality between such BSDEs and SDEs is established.     

On Comparison Theorem and Solutions of BSDEs for Levy Processes

In this paper, we consider backward stochastic differential equations driven by a Levy process. A comparison theorem and an existence and uniqueness theorem of BSDEs with non-Lipschitz coefficients are obtained.     

关于(y,z,u)受限制的带跳倒向随机微分方程的最小g-上解

本文讨论在一般化的右连续信息流完备概率空间中 ,由 Brownian运动和 Poisson过程联合驱动的带跳倒向随机微分方程 (JBSDE) :Yt=ξ + ∫Ttg(s,Ys,Zs,Us) ds- ∫Tt Zsd Ws- ∫Tt∫EUs(e) N(ds,de) + AT - At在漂移系数不满足 L ipschitz条件且关于 (y,z,u)受限制时的最小 g-上解     

带跳倒向随机微分方程最小g-上解

对带跳和一个右连左极的增过程作为惩罚项的倒向随机微分方程定义$g$\,-上解, 并得到极限定理, 作为其应用, 在变量$(y,z,q)$受限条件下, 讨论该方程的最小$g$\,-上解存在唯一性.     

Multidimensional BSDEs with weak monotonicity and general growth generators

This paper aims at solving a multidimensional backward stochastic differential equation （BSDE） whose generator g satisfies a weak monotonicity condition and a general growth condition in y. We first establish an existence and uniqueness result of solutions for this kind of BSDEs by using systematically the technique of the priori estimation, the convolution approach, the iteration, the truncation and the Bihari inequality. Then, we overview some assumptions related closely to the monotonieity condition in the literature and compare them in an effective way, which yields that our existence and uniqueness result really and truly unifies the Mao condition in y and the monotonieity condition with the general growth condition in y, and it generalizes some known results. Finally, we prove a stability theorem and a comparison theorem for this kind of BSDEs, which also improves some known results.     

连续系数倒向随机微分方程最小解的Levi定理

本文研究了倒向随机微分方程解的连续依赖性问题.利用文献[4]中使用的方法,提出并证明了连续系数的一维倒向随机微分方程最小解的Levi定理,推广了文献[10]中的相应结果.     

倒向随机微分方程生成元的表示定理及其应用

本文建立了关于局部L2-有界的倒向随机微分方程生成元的表示定理,此定理推广了Co-quet等人的一个结果.应用该定理,本文给出了倒向随机微分方程的生成元是凹生成元的一个充分必要条件.     

A generalized existence theorem of backward doubly stochastic differential equations

In this paper, we deal with a class of one-dimensional backward doubly stochastic differential equations （BDSDEs）. We obtain a generalized comparison theorem and a generalized existence theorem of BDSDEs.     

Properties of Solutions of BSDEs with Integrable Parameters

The main result of this study is to obtain,using the localization method in Briand et al.Levi,Fatou and Lebesgue type theorems for the solutions of certain one-dimensional backward stochastic differentialequation(BSDEs)with integrable parameters with respect to the terminal condition.     

关于倒向随机微分方程生成元的逆比较定理

Coquet等人在g(t,y ,0 )≡ 0的条件下建立了一个关于倒向随机微分方程生成元g的逆比较定理 .本文对一般的倒向随机微分方程的生成元以及对L2 有界的生成元分别得到了两个新的逆比较定理 .     

带有确定生成元的倒向随机微分方程的共单调定理

对倒向随机微分方程(简记BSDE)的解(y,z),利用Malliavin微分的方法进行了研究．给出了某些关于比较z的方法,在此基础上继续研究(y,z)的某些重要性质,同时推广了Chen Zengjing等人文章中相应的结论．     

系数为左Lipschitz的倒向随机微分方程解的存在性

考虑一类一维倒向随机微分方程(BSDE),其系数关于y满足左Lipschitz条件(可能是不连续的),关于z满足Lipschitz条件.在这样的条件下,证明了BSDE的解是存在的,并且得到了相应的比较定理.     

倒向随机微分方程的一个一般的反比较定理

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.     

Backward doubly stochastic differential equations with weak assumptions on the coefficients

In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs). We obtain existence theorems and comparison theorems for solutions of BDSDEs with weak assumptions on the coefficients.     

Existence and uniqueness result for multidimensional BSDEs with generators of Osgood type

This paper is interested in solving a multidimensional backward stochastic differential equation (BSDE) whose generator satisfies the Osgood condition in y and the Lipschitz condition in z. We establish an existence and uniqueness result of solutions for this kind of BSDEs, which generalizes some known results.     

有限或无限时间终端多维倒向随机微分方程L~1解的存在唯一性(英文)

建立具有可积参数和有限或无限时间终端的多维倒向随机微分方程(BSDEs)解的一个存在唯一性结果,其中生成元g关于y和z均满足对t不一致的Lipschitz连续条件.通过建立解的先验估计证明解的唯一性,然后通过Picard迭代证明解的存在性.