Stochastic differential games with reflection and related obstacle problems for Isaacs equations
Stochastic differential games with reflection and related obstacle problems for Isaacs equations
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艾萨克斯方程的反射随机微分博弈和相关障碍问题
DOI：
10.1007/s10255-011-0068-8
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发表时间：
2007-07
影响因子：
0.8
通讯作者：
Juan Li
中科院分区：
文献类型：
--
作者：
R. Buckdahn;Juan Li
本文首先利用反射倒向随机微分方程（RBSDEs）理论研究了带反射的零和二人随机微分对策。我们将以一种直观的方式建立这类带反射的随机微分对策的上、低值函数的动态规划原理。然后证明了上、下值函数分别是相应的带障碍的上、下Hamilton-Jacobi-Bellman-Isaacs方程的唯一粘性解.该方法显着不同于那些用于控制问题的反射，与新技术开发的兴趣本身。此外，我们还证明了一个新的RBSDES估计，它比El Karoui，Kapoudjian，Pardoux，Peng和Quenez（1997）的估计更精确，这是非常有用的，因为它允许我们通过向前驱动方程初值距离的p次方来估计两个不同RBSDES解的Lp距离.我们还证明了用惩罚方法构造的近似Isaacs方程的唯一粘性解收敛于带障碍的Isaacs方程的粘性解。
In this paper we first investigate zero-sum two-player stochastic differential games with reflection, with the help of theory of Reflected Backward Stochastic Differential Equations (RBSDEs). We will establish the dynamic programming principle for the upper and the lower value functions of this kind of stochastic differential games with reflection in a straightforward way. Then the upper and the lower value functions are proved to be the unique viscosity solutions to the associated upper and the lower Hamilton-Jacobi-Bellman-Isaacs equations with obstacles, respectively. The method differs significantly from those used for control problems with reflection, with new techniques developed of interest on its own. Further, we also prove a new estimate for RBSDEs being sharper than that in the paper of El Karoui, Kapoudjian, Pardoux, Peng and Quenez (1997), which turns out to be very useful because it allows us to estimate theLp-distance of the solutions of two different RBSDEs by thep-th power of the distance of the initial values of the driving forward equations. We also show that the unique viscosity solution to the approximating Isaacs equation constructed by the penalization method converges to the viscosity solution of the Isaacs equation with obstacle.
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DOI：
10.1137/060671954
发表时间：
2007-02
期刊：
SIAM J. Control. Optim.
影响因子：
--
作者：
R. Buckdahn;Juan Li
通讯作者：
R. Buckdahn;Juan Li
影响因子：
6.4
作者：
L. Rogers
通讯作者：
L. Rogers
DOI：
10.2307/2289894
发表时间：
1987
期刊：
Elearn
影响因子：
--
作者：
I. Karatzas
通讯作者：
I. Karatzas
影响因子：
1.6
作者：
El Karoui, N;Peng, S;Quenez, MC
通讯作者：
Quenez, MC
DOI：
10.1137/050642204
发表时间：
2007-06
期刊：
SIAM J. Control. Optim.
影响因子：
--
作者：
Shanjian Tang;S. Hou
通讯作者：
Shanjian Tang;S. Hou