We consider the downlink resource allocation for a multi-carrier-based asynchronous cognitive radio network with statistical knowledge of the channel state information of both primary and secondary systems available at the secondary base station. The problem of secondary utility maximization is investigated under primary and secondary user outage constraints and total power constraint. Analyses are provided for cases where both primary and secondary systems are utilizing either orthogonal frequency-division multiplexing or filter-bank based multi-carrier modulations. The highly complex yet challenging and non-convex joint power-subcarrier allocation problem is tackled by leveraging the principle of alternating optimization techniques. A per-carrier outage-based solution is provided for the subcarrier allocation stage. In the second stage, we introduce an upper bound to the outage constraints to ensure tractability. We propose an efficient convex approximation method to obtain near-optimal solutions of the centralized power control problem. Furthermore, to reduce computational complexity, a distributed implementation based on dual decomposition method is designed. Extensive simulation results are further provided to corroborate the validity of the theoretical findings and demonstrate the effectiveness of the proposed algorithms.