In recent years, the use of Unmanned Aerial Vehicles (UAVs) equipped with Mobile Edge Computing (MEC) servers to provide computational resources to mobile devices(MDs) has emerged as a promising technology. This paper aims to investigate a UAV-assisted Mobile Edge Computing (MEC) system in dynamic scenarios with stochastic computing tasks. Our goal is to minimize the total energy consumption of MDs by optimizing user association, resource allocation, and UAV trajectory. Considering the nonconvexity of the problem and the coupling among variables, we propose a novel deep reinforcement learning algorithm called improved-DDPG. In this algorithm, we employ improved Prioritized Experience Replay (PER) to enhance the convergence of the training process, and we introduce the annealing concept to enhance the algorithm's exploration capability. Simulation results demonstrate that the improved-DDPG algorithm exhibits good convergence and stability. Compared to baseline approaches, the improved-DDPG algorithm effectively reduces the energy consumption of terminal devices.