For the two classes of stochastic processes, namely, martingale difference sequences withconstant conditional variances and processes with independent increments, each square-inte-grable functional of the process has ...For the two classes of stochastic processes, namely, martingale difference sequences withconstant conditional variances and processes with independent increments, each square-inte-grable functional of the process has been shown to have chaos decomposition if and only ifthe process has the property of predictable representation. The definition of chaos is thesame as P. A. Meyer’s, that is polynomial functional in discrete parameter case and ortho-gonal stochastic multiple integral in continuous parameter case. The proofs mainly rely onthe necessary and sufficient conditions for the property of predictable representation forthese two classes of processes, obtained previously by the authors.展开更多
The article first studies the fully coupled Forward-Backward Stochastic Differential Equations （FBSDEs） with the continuous local martingale. The article is mainly divided into two parts. In the first part, it consi...The article first studies the fully coupled Forward-Backward Stochastic Differential Equations （FBSDEs） with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations （BSDEs） with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions.展开更多
预测状态表示(Predictive State Representations,PSRs)是用于解决局部可观测问题的有效方法.然而,现实环境中,通过样本学习得到的PSR模型不可能完全准确.随着计算步数的增多,利用PSR模型计算得到的预测向量有可能越来越偏离其真实值,...预测状态表示(Predictive State Representations,PSRs)是用于解决局部可观测问题的有效方法.然而,现实环境中,通过样本学习得到的PSR模型不可能完全准确.随着计算步数的增多,利用PSR模型计算得到的预测向量有可能越来越偏离其真实值,进而导致PSR模型的预测精度越来越低.文中提出了一种PSR模型的复位算法.通过使用判别分析方法确定系统所处的PSR状态,文中所提算法可对利用计算获取的预测向量复位,从而提高PSR模型的准确性.实验结果表明,采用复位算法的PSR模型在预测精度上明显优于未采用复位算法的PSR模型,验证了所提算法的有效性.展开更多
预测状态表示(predictive state representations,PSR)是一种新型的动态系统模型,用动作-观察值序列的预测向量来表示系统的状态以及预测未来事件发生的概率。综述了预测状态表示的基本原理,对其建模算法进行比较,并概括其最新的应用拓...预测状态表示(predictive state representations,PSR)是一种新型的动态系统模型,用动作-观察值序列的预测向量来表示系统的状态以及预测未来事件发生的概率。综述了预测状态表示的基本原理,对其建模算法进行比较,并概括其最新的应用拓展,最后指出其发展方向。展开更多
基金Supported by the National Natural Science Foundation of China.
文摘For the two classes of stochastic processes, namely, martingale difference sequences withconstant conditional variances and processes with independent increments, each square-inte-grable functional of the process has been shown to have chaos decomposition if and only ifthe process has the property of predictable representation. The definition of chaos is thesame as P. A. Meyer’s, that is polynomial functional in discrete parameter case and ortho-gonal stochastic multiple integral in continuous parameter case. The proofs mainly rely onthe necessary and sufficient conditions for the property of predictable representation forthese two classes of processes, obtained previously by the authors.
文摘The article first studies the fully coupled Forward-Backward Stochastic Differential Equations （FBSDEs） with the continuous local martingale. The article is mainly divided into two parts. In the first part, it considers Backward Stochastic Differential Equations （BSDEs） with the continuous local martingale. Then, on the basis of it, in the second part it considers the fully coupled FBSDEs with the continuous local martingale. It is proved that their solutions exist and are unique under the monotonicity conditions.
文摘预测状态表示(Predictive State Representations,PSRs)是用于解决局部可观测问题的有效方法.然而,现实环境中,通过样本学习得到的PSR模型不可能完全准确.随着计算步数的增多,利用PSR模型计算得到的预测向量有可能越来越偏离其真实值,进而导致PSR模型的预测精度越来越低.文中提出了一种PSR模型的复位算法.通过使用判别分析方法确定系统所处的PSR状态,文中所提算法可对利用计算获取的预测向量复位,从而提高PSR模型的准确性.实验结果表明,采用复位算法的PSR模型在预测精度上明显优于未采用复位算法的PSR模型,验证了所提算法的有效性.
