Critical Behavior in Almost Sure Central Limit Theory

A note on the almost sure limit theorem for self-normalized partial sums of random variables in the domain of attraction of the normal law

“…Some ASCLT results for partial sums were obtained by Lacey and Philipp [4], Ibragimov and Lifshits [5], Miao [6], Berkes and Csáki [7], Hörmann [8], Wu [9,10], and Ye and Wu [11]. Huang and Zhang [12] and Zhang and Yang [13] obtained ASCLT results for self-normalized version.…”

Almost sure local central limit theorem for the product of some partial sums of negatively associated sequences

“…random variables to strongly mixing random variables. We refer the reader to Berkes and Csáki [14], Hörmann [15], Wu [16], Xu and Wu [17], and Tan and Liu [18] for ASCLT.…”

An extension of almost sure central limit theorem for the maximum of stationary Gaussian random fields

“…Some ASCLT results for partial sums were obtained by Lacey and Philipp (1990), Ibragimov and Lifshits (1998), Miao (2008), Berkes and Csáki (2001), Hörmann (2007), and Wu (2011aWu ( ,b, 2012a; Wu and Chen (2013). Fahrner and Stadtmüller (1998) investigated AS-CLT for the maxima of i.i.d.…”