Protuberance effect in the generalized functional Strassen-Révész law

Abstract

The set of increments of the Wiener process

$$V_T = \left\{ {a^{ - 1/2} [W(\tau + a_T \cdot ) - W(\tau )]/L_T , 0 \leqslant \tau \leqslant T - a_T } \right\}$$

, where a_T∈(0,T) and L_T=(2[log(T/a_T)+loglogT])^1/2 is considered. Under the assumptionlog(T/a_T)/loglogT→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.