Large Language Model (LLM) agents increasingly operate across domains such as robotics, virtual assistants, and web automation. However, their stochastic decision-making introduces safety risks that are difficult to anticipate during execution. Existing runtime monitoring frameworks, such as AgentSpec, primarily rely on reactive safety rules that detect violations only when unsafe behavior is imminent or has already occurred, limiting their ability to handle long-horizon dependencies. We present ProbGuard, a proactive runtime monitoring framework for LLM agents that anticipates safety violations through probabilistic risk prediction. ProbGuard abstracts agent executions into symbolic states and learns a Discrete-Time Markov Chain (DTMC) from execution traces to model behavioral dynamics. At runtime, the monitor estimates the probability that execution will remain safe from the current state, and triggers an intervention when this probability falls below a user-defined threshold. To improve robustness, ProbGuard incorporates semantic validity constraints in the abstraction and admits a PAC-style analysis that characterizes the sample complexity required to certify the learned model under standard assumptions. We evaluate ProbGuard in two safety-critical domains: autonomous driving and embodied household agents. Across evaluated scenarios, ProbGuard consistently predicts traffic law violations and collisions in advance, with warnings up to 15.84 seconds at a threshold yielding no false alarms, and up to 38.66 seconds at stricter thresholds. In embodied agent tasks, ProbGuard's re-prompting intervention mode reduces unsafe behavior by 65.37% relative to the unmonitored baseline while retaining 80.4% of the baseline task completion; a stricter halting configuration reduces unsafe behavior by 93.60% at a larger cost in completion.

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