“…The classical method, as illustrated in Heyde [6], Spȃtaru [12], Gut and Spȃtaru [3], etc., proceeds with the assumption that X is in the domain of attraction of a stable law, and uses a version of the powerful Fuk-Nagaev inequality (see Spȃtaru [12]). This inequality is applicable only if the working condition has the form E |X| r < ∞ for some r. The second approach, introduced and practised by Gut and Spȃtaru [4], and Spȃtaru [13], is suitable for cases when Fuk-Nagaev type inequalities prove useless. It assumes existence of finite variance, and after the first step, it goes on via truncation and departure from normality.…”