The paper contains a "smoothed" one-step triangular array asymptotic expansion for discrete-time martingales. An important element of the proof is a second-order description of Skorokhod embedding of discrete martingales in continuous ones. An application to Markov processes is given, along with a bootstrapping example.
Per Aslak Mykland. "Asymptotic Expansions for Martingales." Ann. Probab. 21 (2) 800 - 818, April, 1993. https://doi.org/10.1214/aop/1176989268