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This paper provides a theoretical framework of energy-optimal mobile cloud computing under stochastic wireless channel. Our objective is to conserve energy for the mobile device, by optimally executing mobile applications in the mobile device (i.e., mobile execution) or offloading to the cloud (i.e., cloud execution). One can, in the former case sequentially reconfigure the CPU frequency; or in the latter case dynamically vary the data transmission rate to the cloud, in response to the stochastic channel condition. We formulate both scheduling problems as constrained optimization problems, and obtain closed-form solutions for optimal scheduling policies. Furthermore, for the energy-optimal execution strategy of applications with small output data (e.g., CloudAV), we derive a threshold policy, which states that the data consumption rate, defined as the ratio between the data size (L) and the delay constraint (T), is compared to a threshold which depends on both the energy consumption model and the wireless channel model. Finally, numerical results suggest that a significant amount of energy can be saved for the mobile device by optimally offloading mobile applications to the cloud in some cases. Our theoretical framework and numerical investigations will shed lights on system implementation of mobile cloud computing under stochastic wireless channel.