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This article surveys recent advancements in strategy designs for persistent robotic surveillance tasks, with a focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way, where the efficiency is defined with respect to relevant underlying performance metrics. We start by reviewing the basics of Markov chains, which are the primary motion models for stochastic robotic surveillance. We then discuss the two main criteria regarding thedoi:10.1146/annurev-control-071520-120123 fatcat:kkn5mnjsyva6npgmuvt65ecppy