The paper develops a one-step triangular array asymptotic expansion for continuous martingales which are asymptotically normal. Mixing conditions are not required, but the quadratic variations of the martingales must satisfy a law of large numbers and a central limit type condition. From this result we derive expansions for the distributions of estimators in asymptotically ergodic differential equation models, and also for the bootstrapping estimators of these distributions.
"Asymptotic Expansions and Bootstrapping Distributions for Dependent Variables: A Martingale Approach." Ann. Statist. 20 (2) 623 - 654, June, 1992. https://doi.org/10.1214/aos/1176348649