摘要
This paper considers the rational expectations model with multiplicative noise and input delay,where the system dynamics rely on the conditional expectations of future states.The main contribution is to obtain a sufficient condition for the exact controllability of the rational expectations model.In particular,we derive a sufficient Gramian matrix condition and a rank condition for the delay-free case.The key is the solvability of the backward stochastic difference equations with input delay which is derived from the forward and backward stochastic system.
基金
supported by the National Natural Science Foundation of China under Grants 61821004,62250056,62350710214,U23A20325,62350055
the Natural Science Foundation of Shandong Province,China(ZR2021ZD14,ZR2021JQ24)
High-level Talent Team Project of Qingdao West Coast New Area,China(RCTD-JC-2019-05)
Key Research and Development Program of Shandong Province,China(2020CXGC01208)
Science and Technology Project of Qingdao West Coast New Area,China(2019-32,2020-20,2020-1-4).
