The Open Radio Access Network (O-RAN)-compliant solutions often lack crucial details for implementing effective control loops at various time scales. To overcome this, we introduce MAREA, an O-RAN-compliant mathematical framework designed for the allocation of radio resources to multiple ultra-Reliable Low Latency Communication (uRLLC) services. In the near-real-time (RT) control loop, MAREA employs a novel Martingales-based model to determine the guaranteed radio resources for each uRLLC service. Unlike traditional queueing theory approaches, this model ensures that the probability of packet transmission delays exceeding a predefined threshold -- the violation probability -- remains below a target tolerance. Additionally, MAREA uses a real-time control loop to monitor transmission queues and dynamically adjust guaranteed radio resources in response to traffic anomalies. To the best of our knowledge, MAREA is the first O-RAN-compliant solution that leverages Martingales for both near-RT and RT control loops. Simulations demonstrate that MAREA significantly outperforms reference solutions, achieving an average violation probability that is x10 lower.

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