Abstract-We present a novel dynamic duty cycling scheme to maintain stochastic consistency for caches in sensor networks. To reduce transmissions, base stations often maintain caches for erratically changing sensor sources. Stochastic consistency guarantees the cache-source deviation is within a pre-specified bound with a certain confidence level. We model the erratic sources as Brownian motions, and adaptively predict the next cache update time based on the model. By piggybacking the next update time in each regular data packet, we can dynamically adjust the relaying nodes' duty cycles so that they are awake before the next update message arrives, and are sleeping otherwise. Through simulations on the ns-2 simulator, we show that our approach can achieve very high sourcecache fidelity with low power consumption on many reallife sensor data. On average, our approach consumes 4-5 times less power than GAF [1], and achieves 50% longer network lifetime.