Trajectory-free identifiability and stability of expected hitting times in controlled absorbing Markov processes

Trajectory-level data is widely considered indispensable for recovering global dynamical quantities in stochastic control and reinforcement learning. This paper challenges that assumption by studying controlled absorbing Markov processes under an extreme observational regime where each trajectory is reduced to a single transition, with no temporal links connecting observations. Our contribution is a non-sequential sampling framework: under full support of the predecessor distribution, independent one-step pairs identify the transition submatrix Q row by row through conditional frequencies. The Neumann series is then evaluated algebraically, not term by term. This reframing clarifies that identifiability does not require trajectory-level information, but does require labeled transitions. Despite this severe information constraint, we prove that the expected hitting time remains identifiable from aggregated one-step observations under suitable coverage and persistence conditions. Our main contribution is a unified theoretical framework establishing four interlocking results: identifiability from first-order statistics alone; Lipschitz stability with explicit constants depending only on estimable quantities; structural bounds showing how persistence and drift jointly control the global dynamics; and a concentration phenomenon whereby hitting times are dominated by high-persistence states. The framework extends to absorption probabilities and discounted value functions. These results demonstrate that certain global dynamical quantities remain recoverable under substantially weaker temporal information than traditionally assumed. We also connect the framework to limit theorems for additive functionals of Markov chains and to inference under partial observations, and we outline semi-Markovian and spatially dependent extensions. The identifiability results are established under a fixed stationary policy, with observations of the form ( X pre , X post ) between labeled states. Extending the framework to control requires observing the actions jointly with the state transitions.