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国家自然科学基金(11071145)

作品数:7 被引量:17H指数:3
相关作者:石玉峰林乾朱庆峰王鑫更多>>
相关机构:山东大学山东财经大学更多>>
发文基金:国家自然科学基金国家重点基础研究发展计划山东省自然科学基金更多>>
相关领域:理学更多>>

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Forward-backward doubly stochastic differential equations and related stochastic partial differential equations被引量:6
2012年
The notion of bridge is introduced for systems of coupled forward-backward doubly stochastic differential equations (FBDSDEs). It is proved that if two FBDSDEs are linked by a bridge, then they have the same unique solvability. Consequently, by constructing appropriate bridges, we obtain several classes of uniquely solvable FBDSDEs. Finally, the probabilistie interpretation for the solutions to a class of quasilinear stochastic partial differential equations (SPDEs) combined with algebra equations is given. One distinctive character of this result is that the forward component of the FBDSDEs is coupled with the backvzard variable.
ZHU QingFengSHI YuFeng
关键词:BRIDGE
Peng g-期望下的大数定律被引量:5
2012年
Peng于1997年通过倒向随机微分方程引入了一类性质很好的非线性数学期望,即g-期望.本文中,我们将给出Pengg-期望下的弱大数定律与强大数定律.
林乾石玉峰
关键词:G-期望倒向随机微分方程
Maximum Principle for Partially Observed Optimal Control of Backward Doubly Stochastic Systems
<正>The partially observed control problem is considered for backward doubly stochastic systems with control en...
ZHU Qingfeng~(1,2),WANG Tianxiao~2,SHI Yufeng~2 1.School of Statistics and Mathematics,Shandong University of Finance,Jinan 250014,P.R.China 2.School of Mathematics,Shandong University,Jinan 250100,P.R.China
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带跳的倒向重随机系统的最大值原理及其应用
2013年
本文研究带跳的倒向重随机系统的随机控制问题的最优性条件.在控制域为凸且控制变量进入所有系数条件下,分别以局部形式和全局形式给出必要性最优条件和充分性最优条件.把上述最大值原理应用于重随机线性二次最优控制问题,得到唯一的最优控制,并且给出应用的例子.
朱庆峰王鑫石玉峰
关键词:最优控制POISSON过程
A Class of Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients被引量:3
2014年
In this work the existence of solutions of one-dimensional backward doubly stochastic differential equations (BDSDEs) with coefficients left-Lipschitz in y (may be discontinuous) and Lipschitz in z is studied. Also, the associated comparison theorem is obtained.
Qing-feng ZHUYu-feng SHI
Backward Doubly Stochastic Differential Equations with Jumps and Stochastic Partial Differential-Integral Equations被引量:5
2012年
Backward doubly stochastic differential equations driven by Brownian motions and Poisson process (BDSDEP) with non-Lipschitz coefficients on random time interval are studied. The probabilistic interpretation for the solutions to a class of quasilinear stochastic partial differential-integral equations (SPDIEs) is treated with BDSDEP. Under non-Lipschitz conditions, the existence and uniqueness results for measurable solutions to BDSDEP are established via the smoothing technique. Then, the continuous depen- dence for solutions to BDSDEP is derived. Finally, the probabilistic interpretation for the solutions to a class of quasilinear SPDIEs is given.
Qingfeng ZHUYufeng SHI
Linear quadratic stochastic integral games and related topics被引量:1
2015年
This paper studies linear quadratic games problem for stochastic Volterra integral equations(SVIEs in short) where necessary and sufficient conditions for the existence of saddle points are derived in two different ways.As a consequence,the open problems raised by Chen and Yong(2007) are solved.To characterize the saddle points more clearly,coupled forward-backward stochastic Volterra integral equations and stochastic Fredholm-Volterra integral equations are introduced.Compared with deterministic game problems,some new terms arising from the procedure of deriving the later equations reflect well the essential nature of stochastic systems.Moreover,our representations and arguments are even new in the classical SDEs case.
WANG TianXiaoSHI YuFeng
L^p Solutions of Backward Stochastic Volterra Integral Equations被引量:1
2012年
This paper is devoted to the unique solvability of backward stochastic Volterra integral equations (BSVIEs, for short), in terms of both M-solution and the adapted solutions. We prove the existence and uniqueness of M-solutions of BSVIEs in Lp (1 〈 p 〈 2), which extends the existing results on M-solutions. The unique solvability of adapted solutions of BSVIEs in Lp (p 〉 1) is also considered, which also generalizes the results in the existing literature.
Tian Xiao WANG
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