The paper studies the closed supply chain coordination considering the manufacturer's recycling behavior under asymmetric information. The recovery rate changes dynamically with time and the manufacturer's remanufactured cost information is privates. By constructing a decentralized decision model, the optimal equilibrium solution is obtained and the wholesale price contract is introduced to prompt the manufacturer to transmit the real cost information. The stochastic evolution process of recovery rate is described by using Ito process. The influence of parameters such as information hiding degree and recovery rate on the supply chain are analyzed by numerical simulation. Studies show that the recovery rate reaches a stable value in a short period of time, which fluctuates around the stable value because of the uncertainty fluctuates. External incentives improve recovery rates more than external constraints. Information concealment will reduce manufacturer's recycling rate and public profit and retailer's profit. The wholesale price contract can effectively improve the profit of supply chain members, reduce the loss caused by decentralized decision-making and information asymmetry, and achieve a Pareto improvement.