General Martingale Characterization of G-Brownian Motion

The objective of this article is to derive a general martingale characterization of G-Brownian motion, which generalizes the results obtained in Xu [17 Xu , J. 2010 . Martingale property and capacity under G-framework . Electronic Journal of Probability 15 : 2041 – 2068 .[Web of Science ®] , [Google Scholar]]. For this end, we first study some extensions of stochastic calculus with respect to G-martingales under the sublinear expectation spaces.     

������ϣ��������G-�����˶����������΢�ַ��̵����ƽ��ԭ���о�

This paper concerns stochastic differential equationsdriven by G-Brownian motion under non-Lipschitz condition which is a much weakercondition with a wider range of applications. Stochastic averaging is establishedfor such non-Lipschitz SDEs where an averaged system is presented to replace theoriginal one in the sense of mean square. An example is presented to illustratethe averaging principle.     

Harnack Inequality and Applications for SDEs Driven by G-Brownian Motion

Acta Mathematicae Applicatae Sinica, English Series - In this paper, Wang’s Harnack and shift Harnack inequality for a class of stochastic differential equations driven by G-Brownian motion...     

L—Fuzzy集表现定理

简化文[1]引入的L－集合套概念的条件,并借助文[2]的结论给出L－Fuzzy表现定理的几种形式,进一步揭示普通集合簇与L－Fuzzy集之间的良好对应关系。     

软代数的表示定理

本文研究了集对代数,证明了集对代数是Ｆｕｚｙ格。通过引入强素理想与强素滤的概念,证明了软代数的表示定理：定义了至多只有一个不动点的复原映射的格为软代数的充要条件是它具有同构集对表示。由表示定理可得任一软代数都具有集对表示     

Backward Stochastic Differential Equations Driven by G-Brownian Motion with Double Reflections

Journal of Theoretical Probability - In this paper, we study the reflected backward stochastic differential equations driven by G-Brownian motion with two reflecting obstacles, which means that the...     

Hyperseparoids: A Representation Theorem

In this note, hyperseparoids are introduced; hyperseparoids are to separoids as Tverberg’s theorem is to Radon’s theorem. Also, a geometric representation theorem for acyclic k-separoids is presented which generalises that for separoids exhibited in Bracho and Strausz (Period. Math. Hung. 53:115–120, 2006).     

The Cocycle Property of Stochastic Differential Equations Driven by G-Brownian Motion

In this paper,solutions of the following non-Lipschitz stochastic differential equations driven by G-Brownian motion:X_t=x+∫~t_0b(s,w,X_s)ds+∫~t_0h(s,ω,X_s)dBs+∫~t_0σ(s,ω,X_s)dB_s are constructed.It is shown that they have the cocycle property.Moreover,under some special non-Lipschitz conditions,they are bi-continuous with respect to t,x.     

G-Brown运动驱动的非线性随机时滞微分方程的稳定化

研究了一类G-Brown运动驱动的非线性随机时滞微分方程的稳定化问题.首先,在一个不稳定的G-Brown运动驱动的非线性随机时滞微分方程的漂移项中设计了时滞反馈控制, 得其相应的控制系统.其次, 利用Lyapunov函数方法给出其相应的控制系统是渐近稳定的充分条件.最后, 通过例子说明了所得的结果.     

Large Deviations for Backward Stochastic Differential Equations Driven by G-Brownian Motion

Journal of Theoretical Probability - In this paper, we consider forward–backward stochastic differential equation driven by G-Brownian motion (G-FBSDEs in short) with small parameter...     

V-quantale的表示定理

研究了V-quantale上的(+)和→运算, 得到了强德摩根律的等价刻画; 最后, 给出了V-quantale的表示定理.     

Backward Stochastic Differential Equations Driven by G-Brownian Motion with Uniformly Continuous Generators

Journal of Theoretical Probability - The present paper is devoted to investigating the existence and uniqueness of solutions to a class of non-Lipschitz scalar-valued backward stochastic...     

Representation of Numerical Semigroups by Dyck Paths

We introduce square diagrams that represent numerical semigroups and we obtain an injection from the set of numerical semigroups into the set of Dyck paths.     

广义（N）-模糊积分的转换与表示定理

针对模糊测度空间上由一般可测函数所定义的广义(N)-模糊积分,结合该模糊积分与Lebesgue积分的内在联系,利用α-截断函数的定义,分别首次获得这种广义(N)-模糊积分的积分转换定理和表示定理.     

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.     

Existence and Stability of Solutions to Highly Nonlinear Stochastic Differential Delay Equations Driven by G-Brownian Motion

Under linear expectation(or classical probability), the stability for stochastic differential delay equations(SDDEs), where their coeficients are either linear or nonlinear but bounded by linear functions, has been investigated intensively. Recently, the stability of highly nonlinear hybrid stochastic differential equations is studied by some researchers. In this paper,by using Peng's G-expectation theory, we first prove the existence and uniqueness of solutions to SDDEs driven by G-Brownian motion(G-SDDEs) under local Lipschitz and linear growth conditions. Then the second kind of stability and the dependence of the solutions to G-SDDEs are studied. Finally, we explore the stability and boundedness of highly nonlinear G-SDDEs.     

Set-indexed Brownian Motion on Increasing Paths

We prove that a square-integrable set-indexed stochastic process is a set-indexed Brownian motion if and only if its projections on all the strict increasing continuous paths are one-parameter time-change Brownian motions. We present some applications.     

Representation Theorem for Mild C-existence Families

As we know,the representation theorem is one of the most important theorems foroperator semigroup theory.The representation theorem for exponentially bounded C-semigroup with dense range R(C) was given in [1 ] ,which was generalized to the casethat C does notnecessarily have dense range(see[2 ] ) .In this paper,more general caseis considered.We get a representation theorem for exponentially bounded mild C-exis-tence families.According to this,a simple proof of a construction theorem for C-s…     

A Representation Theorem for Geometric Morphisms

It it shown that geometric morphisms between elementary toposes can be represented as certain adjunctions between the corresponding categories of locales. These adjunctions are characterized by (i) they preserve the order enrichment and the Sierpiński locale, and (ii) they satisfy Frobenius reciprocity.