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In this paper stochastic downlink power control is presented for wireless networks with time varying channels. Transmit power is assigned so as to jointly consider a user's objective with respect to meeting a performance requirement and the network's objective with respect to the regulation of generated interference. The stochastic nature of the channel gains between transmitters and receivers are taken into account when allocating transmit power. Aside from the random channel between the base station and the users, impairments such as noisy feedback and the loss of feedback from the users to the base station are considered. The presented algorithm has low complexity in requiring information pertaining to the perceived interference of each user, rather than the stochastic values of the link gains. Online implementation is possible with a robust Kalman filter used for interference estimation.