Solution to Delayed Forward and Backward Stochastic Difference Equations and Its Applications

• 成果类型: Article
• 署名作者: Xu, Juanjuan; Wang, Wei; Zhang, Huanshui
• 署名单位: Shandong University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2020.2996236
• 发表日期: 2021
• 页码: 1407-1413
• 关键词: Delay effects; DELAYS; Stochastic processes; games; Mathematical model; Difference equations; optimal control; Forward and backward stochastic difference equations (FBSDEs); leader– follower game; Riccati-like equation; time delay

摘要

In this article, we will study a class of forward and backward stochastic difference equations (discrete-time FBSDEs) with time delay. By establishing a nonhomogeneous relationship between the forward and backward stochastic processes, we give the explicit solution of the discrete-time FBSDEs with time delay in terms of a class of Riccati-like equations. The explicit solution is of great significance in solving the stochastic control problem. To show this point, we study a stochastic leader-follower game problem with input delay. With the derived explicit solution of the discrete-time FBSDEs with time delay, we present the optimal controllers of the leader and the follower in the feedback form of the predictors.