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In this work, the stochastic traffic engineering problem in multihop cognitive wireless mesh networks is addressed. The challenges induced by the random behaviors of the primary users are investigated in a stochastic network utility maximization framework. For the convex stochastic traffic engineering problem, we propose a fully distributed algorithmic solution which provably converges to the global optimum with probability one. We next extend our framework to the cognitive wireless mesh networks with nonconvex utility functions, where a decentralized algorithmic solution, based on learning automata techniques, is proposed. We show that the decentralized solution converges to the global optimum solution asymptotically.