Some "LIM INF" Results for Increments of a Wiener Process
Some "LIM INF" Results for Increments of a Wiener Process
Let $W(t)$ for $0 \leq t < \infty$ be a standard Wiener process, suppose $0 < a_T \leq T$ for $T > 0$, and let $d(T, t) = \{2t\lbrack\log(T/t) + \log \log t \rbrack\}^{1/2}$. Quantities such as $\lim, \inf_{T \rightarrow \infty} \sup_{a_T \leq t \leq T} \frac{W(T) - W(T - …