On Exact Asymptotics in the Weak Law of Large Numbers for Sums of Independent Random Variables with a Common Distribution Function from the Domain of Attraction of a Stable Law

Precise rates in the law of the logarithm in the Hilbert space

“…However, by replacing n 1/p by √ n log log n, Gut and Spȃtaru [13] established an analogous result called the precise asymptotics of the law of the iterated logarithm. Necessary and sufficient conditions for precise asymptotics concerning the LIL were previously obtained by Li, Wang, and Rao [17] and Rozovsky [18]. By replacing n 1/p by √ n log n, Lai [16] and Chow and Lai [4] considered the following result on the law of the logarithm.…”

The asymptotic behavior over a small parameter of a series of large deviation probabilities weighted with the Dirichlet divisors function

“…The same problem for the Spitzer series have been studied in many papers (see, for example, [4], [20], [17], [2]). The problem is not yet solved in a final form, since sufficient conditions used to obtain the asymptotics of the Spitzer series are stronger than the assumption needed for just the convergence of it.…”

Precise asymptotics for a series of T. L. Lai

“…The literature on this so-called precise asymptotics problem is reasonably rich, almost exhaustive references being given in Spȃtaru [13]. (We record here three new papers in the field by Scheffler [11] and Rozovsky [9,10], and recent related work on counting processes, record times, and partial maxima: Gut and Steinebach [5], Gut [2], Wang and Yang [14], and Wang, Yan and Yang [15]. )…”