Between Strassen and Chung normalizations for Lévy's area process (Q1385009)

The aim of this paper is to confirm an analogue of the main result, given by \textit{P. Baldi} and \textit{B. Roynette} [C. R. Acad. Sci., Paris, Sér. I 314, No. 12, 935-940 (1992; Zbl 0751.60074)], in the case of an \(m\)-dimensional Brownian motion, now in the case of Lévy's area process. Let \(\{L(t): t\geq 0\}\) be Lévy's area process, let \(\gamma:\mathbb{R}_+\mapsto\mathbb{R}\), and let \(\{Z_t: t\geq 3\}\) be the process defined by \(Z_t(s) =L(ts)/(2t \log\log t)\), \(0\leq s\leq 1\). Conditions on \(\gamma\) are given such that the set of all limit points of \(\{\gamma (t)Z_t: t\geq 3\}\) as \(t\to\infty\) is a.s. equal to the set of all continuous functions defined on \([0,1]\) which vanish at 0.