关于反射倒向随机微分方程的解的一些性质(英文)

研究了关于反射倒向随机微分方程的解的一些性质.同时在适当的条件下建立了关于反射倒向随机微分方程生成元的一个唯一性定理和一个逆比较定理.     

关于反射倒向随机微分方程的解的一些性质

研究了关于反射倒向随机微分方程的解的一些性质．同时在适当的条件下建立了关于反射倒向随机微分方程生成元的一个唯一性定理和一个逆比较定理．     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Mémin,Peng[1],Coquet,Hu,Mémin,Peng[2],Chen[3],Jiang[8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题.在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题.本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题.     

反射倒向随机微分方程的逆比较问题(Ⅰ)

在Briand,Coquet,Hu,Memin,Peng[1],Coquet,Hu,Memin,Peng[2],Chen[3],Jiang [8]等中,研究了倒向随机微分方程的逆比较定理,就是通过比较倒向随机微分方程的解来比较倒向随机微分方程的生成元问题．在文[9]中Li和Tang首次研究了反射倒向随机微分方程的逆比较问题．本文考虑在更一般的条件下,反射倒向随机微分方程的生成元的逆比较问题．     

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.     

关于倒向随机微分方程生成元惟一性的一个结果

在本文中,在假定倒向随机微分方程的标准参数满足较弱条件的前提下,我们证明了倒向随机微分方程的生成元由相对应的倒向随机微分方程的终端条件所得到的初始值惟一决定.这个结果从另一方面也论证和推广了Peng的推测.     

生成元连续且线性增长的反射倒向随机微分方程生成元的表示定理（英文）

本文建立了一个生成元满足连续且线性增长条件的反射倒向随机微分方程生成元的局部表示定理,此定理推广了一些已有的倒向随机微分方程生成元的表示定理.应用此表示定理,本文获得了一个一般的反射倒向随机微分方程的逆比较定理,同时讨论了此类方程的一些性质.     

由连续半鞅驱动的倒向随机微分方程解的比较定理

彭实戈[1]首先建立了一维倒向随机微分方程的比较定理,本文在Lipschitz条件下研究由连续半鞅驱动的倒向随机微分方程,我们将比较定理推广到此类倒向随机微分方程,并且证明方法比彭实戈[1]的更加直接和简单.     

正倒向随机微分方程解的比较定理

讨论了正倒向随机微分方程解的比较问题.阐述了正倒向随机微分方程在随机最优控制、现代金融理论中的广泛而深刻的应用, 对于一类正倒向随机微分方程, 利用Ito公式、停时等随机分析方法,通过构造辅助正倒向随机微分方程,得到了正倒向随机微分方程解的比较定理.     

多维带跳倒向随机微分方程比较定理

研究了高维及矩阵值带跳倒向随机微分方程解的比较定理问题.利用倒向随机生存性质的相关理论,将比较定理转化为一个特定闭凸集上的生存性质问题,并得到了比较定理成立的一个充分必要条件.     

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In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDEs), whose generators are continuous with linear growth. It generalizes some known representation theorems for generators of backward stochastic differential equations (BSDEs). As some applications, a general converse comparison theorem for RBSDEs is obtained and some properties of RBSDEs are discussed.     

A Converse Comparison Theorem for <Emphasis Type="Italic">g</Emphasis>-Expectations

With the help of a limit property of solutions of backward stochastic differential equations(BSDEs),this paper establishes a converse comparison theorem for deterministic generators g of BSDEs under the assumption g(t, y, 0) ≡0.     

A Relationship Between the Conditional <Emphasis Type="Italic">g</Emphasis>-Evaluation System and the Generator <Emphasis Type="Italic">g</Emphasis> and Its Applications

In this paper, under the most elementary conditions on a backward stochastic differential equation （BSDE for short） introduced by Peng, a new relationship between the conditional g-evaluation system and the generator g of BSDE is obtained in the sense of ＂process＂, based on some recent results of Jiang. Moreover, as applications, two converse comparison theorems and two uniqueness theorems on the generators of BSDEs are proved.     

Lévy过程驱动的BSDE的反比较定理与Jensen不等式

本文研究了由一维Lévy过程驱动的倒向随机微分方程(BSDE)的反比较定理.利用一般g-期望下BSDE的反比较定理的证明方法,推导出了一般f-期望下BSDE的反比较定理,并给出了一般f-期望下Jensen不等式成立的充分必要条件.     

Lp(p > 1) Solutions of BSDEs with Generators Satisfying Some Non-uniform Conditions in t and ω

This paper is devoted to the L^p(p > 1) solutions of one-dimensional backward stochastic differential equations(BSDEs for short) with general time intervals and generators satisfying some non-uniform conditions in t and ω. An existence and uniqueness result,a comparison theorem and an existence result for the minimal solutions are respectively obtained, which considerably improve some known works. Some classical techniques used to deal with the existence and uniqueness of L^p     

Invariant Representation for Stochastic Differential Operator by Bsdes with Uniformly Continuous Coefficients and its Applications

In this paper, we prove that a kind of second order stochastic differential operator can be represented by the limit of solutions of BSDEs with uniformly continuous coefficients. This result is a generalization of the representation for the uniformly continuous generator. With the help of this representation, we obtain the corresponding converse comparison theorem for the BSDEs with uniformly continuous coefficients, and get some equivalent relationships between the properties of the generator g and the associated solutions of BSDEs. Moreover, we give a new proof about g-convexity.     

A converse comparison theorem for anticipated BSDEs and related non-linear expectations

The converse comparison theorem has received much attention in the theory of backward stochastic differential equations (BSDEs). However, no such theorem has been proved for anticipated BSDEs. In this paper, we derive a converse comparison theorem by first giving an existence and uniqueness theorem for adapted solutions of anticipated BSDEs with a stopping time and then related to (f,δ)$(f,\delta )$-expectations induced by anticipated BSDEs.     

One-dimensional BSDEs with finite and infinite time horizons

This paper is devoted to solving one-dimensional backward stochastic differential equations (BSDEs), where the time horizon may be finite or infinite and the assumptions on the generator g are not necessary to be uniform on t. We first show the existence of the minimal solution for this kind of BSDEs with linear growth generators. Then, we establish a general comparison theorem for solutions of this kind of BSDEs with weakly monotonic and uniformly continuous generators. Finally, we give an existence and uniqueness result for solutions of this kind of BSDEs with uniformly continuous generators.     

倒向随机微分方程的Malliavin微分和共单调定理

本文利用Malliavin微分的理论研究了倒向随机微分方程的解$(y,z)$, 首先利用$y$的Malliavin微分得到了一种比较$z$的方法, 然后利用该方法得到了含有随机生成元的倒向随机微分方程的共单调定理.