“…This topic has been studied extensively. For example, Klesov [17] proved that if E[X] = 0, E[X 2 ] > 0 and E[|X| 3 ] < ∞, then [17] with E[|X| q ] < ∞ for some q ∈ (2, 3], He and Xie [14] got a much faster rate for Heyde's result. Recently, Gut and Steinebach [12,13], and Kong [18] also extended the Klesov's [17] result, respectively, and got some new results.…”