Lim inf results for the Wiener process and its increments under the \(L_ 2\)-norm (Q1184046)

Let \(W(t)\) be a Wiener process. The \(\liminf\) behavior of the \(L_ 2\)- norm of \(W(t)\) on the interval \([T-a(T), T]\) and of \(| W(t+\theta T)- W(t)|\) on the interval \([\alpha T,\beta T]\) is given under suitable conditions.