Linear Quadratic Nonzero Sum Differential Games With Random Jumps
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摘要: 对于一类以布朗运动和泊松过程为噪声源的正倒向随机微分方程，在单调性假设下,给出了解的存在性和唯一性的结果．然后将这些结果应用于带随机跳跃的线性二次非零和微分对策问题之中，由上述正倒向随机微分方程的解得到了开环Nash均衡点的显式形式．Abstract: The existence and uniqueness results of the solutions for one kind of forward-backward stochastic differential equations with Brownian motion and Poisson process as the noise source were given under the monotone conditions. Then these results were applied to get the explicit form of the open-loop Nash equilibrium point for nonzero sum differential games problem with random jump by the solution of the forward-backward stochastic differential equations.
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[1] MA Jin,Protter P,YONG Jiong-min.Solving forward-backward stochastic differential equations explicitly—a four step scheme[J].Probab Theory Related Fields,1994,98(2)：339—359. doi: 10.1007/BF01192258 [2] HU Ying,PENG Shi-ge.Solution of forward-backward stochastic differential equations[J].Probab Theory Related Fields,1995,103(2)：273—283. doi: 10.1007/BF01204218 [3] PENG Shi-ge,WU Zhen.Fully coupled forward-backward stochastic differential equations and applications to optimal control[J].SIAM J Control Optim,1999,37(3)：825—843. doi: 10.1137/S0363012996313549 [4] YONG Jiong-min.Finding adapted solution of forward-backward stochastic differential equations-method of continuation[J].Probab Theory Related Fields,1997,107(3)：537—572. doi: 10.1007/s004400050098 [5] TANG Shan-jian,LI Xun-jing.Necessary condition for optimal control of stochastic systems with random jumps[J].SIAM J Control Optim,1994,32(5)：1447—1475. doi: 10.1137/S0363012992233858 [6] SITU Rong.On solution of backward stochastic differential equations with jumps and applications[J].Stochastic Processes and Their Applications,1997,66(2)：209—236. doi: 10.1016/S0304-4149(96)00120-2 [7] WU Zhen.Forward-backward stochastic differential equations with Brownian motion and Poisson process[J].Acta Mathematicae Applicatae Sinica,1999,15(3)：433—443. doi: 10.1007/BF02684045 [8] Friedman A.Differential Games[M].New York:Wiley-Interscience,1971. [9] Bensoussan A.Point de Nash dans de cas de fonctionnelles quadratiques et jeux différentiels N personnes[J].SIAM J Control Optim,1974,12(3):728—742. [10] Eisele T.Nonexistence and nonuniqueness of open-loop equilibria in linear-quadratic differential games[J].J Math Anal Appl,1982,37(3):443—468. [11] Hamadène S.Nonzero sum linear-quadratic stochastic differential games and backward-forward equations[J].Stochastic Anal Appl,1999,17(2):117—130. doi: 10.1080/07362999908809591 [12] Ikeda N,Watanabe S.Stochastic Differential Equations and Diffusion Processes[M].Kodansha:North-Holland,1981. -
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