L 1 bounds for some martingale central limit theorems

On the Wassertein distance for a martingale central limit theorem

“…see (5.3) of Van Dung et al [5]. We give an estimation for the second term in the right-hand side of (14).…”

“…Despite the Kolmogorov distance in central limit theorem has been intensely studied, research of bounds with respect to the Wassertein distance are rare. To the best of our knowledge, we only aware the articles of Van Dung et al [5] and Röllin [6]. Denote by…”

“…the Wassertein distance between the distributions of S n /s n and the standard normal random variable. Van Dung et al [5] extended Mourrat's bounds to the L 1 -bound in the mean central limit theorem, that is, if X ∞ ≤ γ a.s., then for p > 1/2,…”

On quantitative bounds in the mean martingale central limit theorem

“…In contrast, bounds with respect to the Wasserstein distance are rare. To the best of our knowledge, the first result was obtained by Dedecker and Rio (2008) in the case of stationary martingale differences, and later generalised by Van Dung, Son and Tien (2014) under conditions akin to those asserted by Bolthausen (1982).…”

On Wasserstein-1 distance in the central limit theorem for elephant random walk

“…In the sequel, constants C and C p are always numerical constants that may change between appearances. In the proof of Lemma 2.3, we shall use the following technical lemma of Van Dung et al [14].…”