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Spectrum sensing is a critical function for enabling dynamic spectrum access (DSA) in wireless networks that utilize cognitive radio (CR). In DSA networks, unlicensed secondary users can gain access to a licensed spectrum band as long as they do not cause harmful interfere to primary users. Spectrum sensing is subject to errors in the form of false alarms and missed detections. False alarms cause spectrum under-use by secondary users, and missed detections cause interference to primary users. Although existing research has demonstrated the utility of a Markov chain for modeling the spectrum access pattern of primary users over time, little effort has been directed toward spectrum sensing based upon such models. In this paper, we develop general sequence detection algorithms for Markov sources in noise for spectrum sensing in DSA networks. We assign different Bayesian cost factors for missed detections and false alarms, and we show that a suitably modified forward-backward sequence detection algorithm is optimal in minimizing the detection risk. Two advanced sequence detection algorithms, the complete forward algorithm and the complete forward partial backward algorithm are introduced and their performances are compared as well. Along the way, we observe new fundamental limitations on sensing performance that we term the risk floor and the window length limitation of energy detection and coherent detection that arise from mismatch of their observation window with the PU's spectrum access pattern.