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The power control of wireless networks is formulated using a stochastic optimal control framework, in which the evolution of the channel is described by stochastic differential equations (SDEs). The latter capture the spatio-temporal variations of the communication link, as well as the randomness. This class of models is more realistic than the static models usually encountered in the literature. Under this scenario, average and probabilistic Quality of Service (QoS) measures are introduced to evaluate the performance of any control strategy by using Chernoff bounds. Moreover, the Chernoff bound is computed explicitly, while the solution of the stochastic optimal power control is obtained through pathwise optimization. The pathwise optimization can be solved using linear programming if predictable control strategies are introduced. Finally, if predictable control strategies do not hold, it is shown that the proposed power control problem reduces to particular convex optimizations.