This paper presents a Brownian-approximation framework to optimize the quality of experience (QoE) for real-time video streaming in wireless networks. In real-time video streaming, one major challenge is to tackle the natural tension between the two most critical QoE metrics: playback latency and video interruption. To study this trade-off, we first propose an analytical model that precisely captures all aspects of the playback process of a real-time video stream, including playback latency, video interruptions, and packet dropping. Built on this model, we show that the playback process of a real-time video can be approximated by a two-sided reflected Brownian motion. Through such Brownian approximation, we are able to study the fundamental limits of the two QoE metrics and characterize a necessary and sufficient condition for a set of QoE performance requirements to be feasible. We propose a scheduling policy that satisfies any feasible set of QoE performance requirements and then obtain simple rules on the trade-off between playback latency and the video interrupt rates, in both heavy-traffic and under-loaded regimes. Finally, simulation results verify the accuracy of the proposed approximation and show that the proposed policy outperforms other popular baseline policies.