On the Wassertein distance for a martingale central limit theorem

We prove an upper bound on the Wassertein distance between normalized martingales and the standard normal random variable, which extends a result of R"ollin [Statist. Probabil. Lett. 138 (2018) 171-176]. The proof is based on a method of Bolthausen [Ann. Probab. 10 (1982) 672-688].