One more on the convergence rates in precise asymptotics. LV Rozovsky

Let eta(n), n >= 1, be a sequence of random variables. We study conditions under which lim(epsilon SE arrow 0) (Sigma(n >= 1) phi(n) P(eta(n) >= f (epsilon g(n))) - nu(epsilon)) = C, where C is a constant, assuming among other conditions that non-negative functions phi(x) and f (x), g(x), tend, respectively, to 0 and to infinity as x -> infinity. Results obtained, in particular, are wide generalization of the similar results obtained recently in Gut and Steinebach (2013), Kong (2016), Kong and Dai (2016) and Zhang (2019). (C) 2020 Published by Elsevier B.V.