单调性条件下G-Brown运动驱动的倒向随机微分方程

研究了由G-Brown运动驱动的倒向随机微分方程■解的存在唯一性问题.其生成元f关于z是Lipschitz连续的,关于y是线性增长且满足单调性条件.     

Osgood条件下G-Brown驱动的倒向随机微分方程

在生成元关于变量y满足Osgood条件、关于变量z满足Lipschitz条件下,建立了G-Brown运动驱动的倒向随机微分方程的解的存在唯一性定理.     

局部Lipschitz条件下的布朗运动和泊松过程混合驱动的正倒向随机微分方程

本文得到在局部Lipschiz条件下的布朗运动和泊松过程混合驱动的倒向随机微分方程的存在唯一性；同时也证明了布朗运动和泊松过程混合驱动的完全藕合的正倒向随机微分方程在局部Lipschitz条件下的解的存在唯一性。     

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.     

一类倒向随机微分方程L~p解对终值的单调连续性

在生成元g满足关于y单调且关于z Lipschitz连续的条件下,范(2007)得到了倒向随机微分方程L~p解对终值的单调连续结果.在g关于y单调且关于z一致连续的条件下证明了倒向随机微分方程L~p解的单调连续性,推广了范(2007)的工作,并且方法是新的.     

随机Lipschitz条件下一般时间终端的多维BSDE解的存在唯一性

某个新的范数空间上利用压缩映像原理,在生成元g满足对二元组■均不一致的随机Lipschitz条件下,证明了一般时间终端多维倒向随机微分方程(BSDE)解的存在唯一性,作为推论得到了该类倒向随机微分方程解的递归迭代序列的收敛性.     

由Lévy过程驱动的反射型倒向随机微分方程

证明了由Lévy过程驱动的反射型倒向随机微分方程在局部Lipschitz系数下的解的存在唯一性,并且研究了解的稳定性质.此外,当系数满足Lipschitz条件以及反射壁正则时,证明了过程K的正则性.     

非Lipschitz条件下由Levy过程驱动的倒向随机微分方程解的存在唯一及其稳定性

本文研究了由满足某种矩条件下Levy过程相应的Teugel鞅及与之独立的布朗运动驱动的倒向随机微分方程，给出了飘逸系数满足非Lipschitz条件下解的存在唯一及稳定性结论．解的存在性是通过Picard迭代法给出的．解的L^2收敛性是在飘逸系数弱于L^2收敛意义下所得到的。     

非Lipschitz条件下由Lévy过程驱动的倒向随机微分方程解的存在唯一及其稳定性

本文研究了由满足某种矩条件下Lévy过程相应的Teugel鞅及与之独立的布朗运动驱动的倒向随机微分方程,给出了飘逸系数满足非Lipschitz条件下解的存在唯一及稳定性结论.解的存在性是通过Picard迭代法给出的.解的L2收敛性是在飘逸系数弱于L2收敛意义下所得到的.     

由Lévy过程驱动的倒向双重随机微分方程的比较定理及其应用

本文研究了由Lévy过程和与之独立的布朗运动驱动的倒向双重随机微分方程,给出了相应的比较定理.作为比较定理的-个应用,文章证明了由Lévy过程驱动的倒向双重随机微分方程在其系数满足连续线性增长条件下解的存在性,并得到该方程的最小解.     

带跳的分数倒向重随机微分方程及相应的随机积分偏微分方程

本文首次把Poisson随机测度引入分数倒向重随机微分方程,基于可料的Girsanov变换证明由Brown运动、Poisson随机测度和Hurst参数在(1/2,1)范围内的分数Brown运动共同驱动的半线性倒向重随机微分方程解的存在唯一性.在此基础上,本文定义一类半线性随机积分偏微分方程的随机黏性解,并证明该黏性解由带跳分数倒向重随机微分方程的解唯一地给出,对经典的黏性解理论作出有益的补充.     

The Regularity of Stochastic Convolution Driven by Tempered Fractional Brownian Motion and Its Application to Mean-field Stochastic Differential Equations

In this paper, some properties of a stochastic convolution driven by tempered fractional Brownian motion are obtained. Based on this result, we get the existence and uniqueness of stochastic mean-field equation driven by tempered fractional Brownian motion. Furthermore, combining with the Banach fixed point theorem and the properties of Mittag-Leffler functions, we study the existence and uniqueness of mild solution for a kind of time fractional mean-field stochastic differential equation driven by tempered fractional Brownian motion.     

z一致连续的倒向随机微分方程解的一个存在唯一性结果

建立了关于一维倒向随机微分方程(简写为BSDE)的一个存在唯一性结果,其中BSDE的生成元g关于y满足Constantin条件,关于z是一致连续的.这改进了一些已知结果.     

由连续半鞅驱动的倒向随机微分方程

本文引出了连续半驱动的倒向随机微分方程,定义并证明了此类方程解的存在性与唯一性。     

Mixed Stochastic Differential Equations: Existence and Uniqueness Result

In this paper we establish an existence and uniqueness result for solutions of multidimensional, time-dependent, stochastic differential equations driven simultaneously by a multidimensional fractional Brownian motion with Hurst parameter \(H>1/2\) and a multidimensional standard Brownian motion under a weaker condition than the Lipschitz one.     

Reflected backward stochastic differential equation with jumps and RCLL obstacle

In this paper we study one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an independent Poisson point process when the solution is forced to stay above a right continuous left limits obstacle. We prove existence and uniqueness of the solution by using a penalization method combined with a monotonic limit theorem.     

Solutions to BSDEs driven by both standard and fractional Brownian motions

The backward stochastic differential equations driven by both standard and fractional Brownian motions (or, in short, SFBSDE) are studied. A Wick-Itô stochastic integral for a fractional Brownian motion is adopted. The fractional Itô formula for the standard and fractional Brownian motions is provided. Introducing the concept of the quasi-conditional expectation, we study some its properties. Using the quasi-conditional expectation, we also discuss the existence and uniqueness of solutions to general SFBSDEs, where a fixed point principle is employed. Moreover, solutions to linear SFBSDEs are investigated. Finally, an explicit solution to a class of linear SFBSDEs is found.     

Evolution equations driven by a fractional Brownian motion

In this paper we study nonlinear stochastic evolution equations in a Hilbert space driven by a cylindrical fractional Brownian motion with Hurst parameter and nuclear covariance operator. We establish the existence and uniqueness of a mild solution under some regularity and boundedness conditions on the coefficients and for some values of the parameter H. This result is applied to stochastic parabolic equation perturbed by a fractional white noise. In this case, if the coefficients are Lipschitz continuous and bounded the existence and uniqueness of a solution holds if . The proofs of our results combine techniques of fractional calculus with semigroup estimates.     

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.     

带随机初值的随机偏微分方程整体解的存在性

研究了一类带随机初值并且由分数次Brownian运动驱动的随机偏微分方程.借助于Kolmogorov准则,建立了整体Lipschitz条件下此类随机偏微分方程的一个解.同时证明了局部Lipschitz条件下整体解的存在性.