We study the problem of synthesizing strategies for a mobile sensor network to conduct surveillance in partnership with static alarm triggers. We formulate the problem as a multi-agent reactive synthesis problem with surveillance objectives specified as temporal logic formulas. In order to avoid the state space blow-up arising from a centralized strategy computation, we propose a method to decentralize the surveillance strategy synthesis by decomposing the multi-agent game into subgames that can be solved independently. We also decompose the global surveillance specification into local specifications for each sensor, and show that if the sensors satisfy their local surveillance specifications, then the sensor network as a whole will satisfy the global surveillance objective. Thus, our method is able to guarantee global surveillance properties in a mobile sensor network while synthesizing completely decentralized strategies with no need for coordination between the sensors. We also present a case study in which we demonstrate an application of decentralized surveillance strategy synthesis.