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In this paper, the problem of efficient operation of an energy-constrained, heterogeneous Wireless Body Area Network (WBAN) to optimize an activity detection application is addressed. WBANs constitute a new class of wireless sensor networks that enable diverse applications in healthcare, entertainment, sports, military and emergency situations. A typical WBAN consists of a few, heterogeneous sensors wirelessly coupled to an energy-constrained fusion center which, according to observations of a real-world prototype WBAN, imposes critical restrictions on system lifetime. To address this issue, a novel stochastic control framework is introduced, which considers both sensor heterogeneity and application requirements, for achieving the two-fold goal: energy savings with satisfactory detection performance. An optimal dynamic programming algorithm for the sensor selection problem is also derived. Important properties of the cost functionals are derived and used to design three approximation algorithms, which offer near optimal performance with significant complexity reduction. Simulations on real-world data show energy gains as high as 68% in comparison to an equal allocation scheme with probability of detection error on the order of 10-4.