• Liang, Hong (Institute of Applied Mathematics College of Science Northwest A&F University) ;
  • Zhou, Jianjun (Institute of Applied Mathematics College of Science Northwest A&F University)
  • Received : 2019.02.21
  • Accepted : 2019.05.16
  • Published : 2020.03.31


This paper investigates infinite horizon optimal control problems driven by a class of backward stochastic delay differential equations in Hilbert spaces. We first obtain a prior estimate for the solutions of state equations, by which the existence and uniqueness results are proved. Meanwhile, necessary and sufficient conditions for optimal control problems on an infinite horizon are derived by introducing time-advanced stochastic differential equations as adjoint equations. Finally, the theoretical results are applied to a linear-quadratic control problem.


Supported by : Natural Science Foundation of Shaanxi Province, Central Universities


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