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This paper presents a novel stochastic modeling and optimization framework for energy minimization in multicore systems running real-time applications with tolerance to deadline misses. This framework is based on stochastic application models, which capture the variability of and the spatial and temporal correlations among the workloads of concurrent and interdependent tasks that constitute the application. These stochastic models are utilized in novel mathematical formulations to obtain optimal energy management policies. Experimental results on MPEG2 video decoding show that significant energy savings can be achieved, often close to the theoretical upper bound.