Abstract This paper is concerned with a kind of infinite horizon forward and backward stochastic difference equations (FBSDEs) with asymmetric information. The asymmetric information means that there exists two kinds of conditional expectations with respect to two different filtrations caused by the additive noise and the measurement packet dropout. The main contribution is to present the analytical solutions of the FBSDEs with asymmetric information. The key technique is to establish non-homogenous relationship between the backward stochastic process and the estimation of the forward stochastic process. As applications, we obtain the optimal solution to the infinite horizon stochastic linear quadratic (LQ) optimal control with asymmetric information.

中文翻译：

---

信息不对称的正反向随机差分方程的解与应用

摘要 本文研究了一类具有非对称信息的无限水平前向和后向随机差分方程(FBSDEs)。信息不对称意味着对于加性噪声和测量包丢失引起的两种不同过滤，存在两种条件期望。主要贡献是提出具有不对称信息的 FBSDE 的解析解。关键技术是在后向随机过程和前向随机过程的估计之间建立非齐次关系。作为应用，我们获得了具有非对称信息的无限水平随机线性二次（LQ）最优控制的最优解。