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In cognitive radio networks (CRNs), perfect knowledge of a dynamic radio environment is hard to know due to hardware limitation, short sensing time and network connectivity issues in CRNs. In this paper, we study the dynamic resource allocation problem for heterogeneous services in CRNs with imperfect channel sensing. We formulate the optimization problem as a mixed integer programming problem under constraints. Then we solve the optimal joint power and channel allocation problem using discrete stochastic optimization method. The proposed algorithm has low computation complexity and fast convergence to approximate to the optimal solution under imperfect channel sensing. Another advantage of this method is that it can track the changing radio environment to allocate the resources dynamically. Simulation results are presented to demonstrate the effectiveness of the proposed scheme.