To address the growing demand for latency-sensitive Internet of Things (IoT) applications in remote regions, satellite–integrated mobile edge computing (SMEC) deploys computational resources on Low Earth Orbit (LEO) satellites to provide seamless network access and edge computing services for IoT devices lacking terrestrial network coverage. However, ensuring quality of service (QoS) for latency-sensitive tasks in SMEC systems remains challenging due to two critical limitations: existing deterministic models cannot adequately capture the stochastic nature of discontinuous satellite–ground links, leading to inaccurate queuing delay predictions, and current approaches fail to adapt to dynamic user task preferences that significantly impact offloading effectiveness. In response to these challenges, this paper develops a novel dynamic task offloading framework that integrates martingale-based delay analysis with adaptive game-theoretic optimization. We employ Markov Chain Monte Carlo (MCMC) methods to characterize discontinuous satellite–ground stochastic service processes and apply martingale theory to derive tight statistical delay guarantees that significantly outperform conventional moment generating function approaches. Based on this analytical foundation, we formulate multi-task offloading as an exact potential game and propose the Temporal-Enhanced Stochastic Learning (TESL) algorithm, which leverages historical trend learning and environmental dynamics detection to achieve robust convergence in non-stationary environments. Experimental results demonstrate that TESL achieves a 37% lower delay violation probability compared to the best-performing baseline algorithm, exhibiting superior convergence efficiency and adaptability while improving utility, making it well-suited for practical SMEC deployments.
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