Protuberance effect in the generalized Strassen–Révész law

The set increments of the Wiener process
$$ V_T=\{a^{-1/2}[W(\tau+a_T\cdot)-W(\tau)],\ 0\le\tau\le T-a_T\}, $$
$L_T=(2[\log(T/a_T)+\log\log T])^{1/2}$ is considered. Under assumption $\log(T/a_T)/\log\log T\to c$ the set $V_T$ oscillates between $b\mathbb K$ and $\mathbb K$, where $b=[c/(c+1)]^{1/2}$ and $\mathbb K$ is the Strassen ball. Bibliography: 9 titles.