How big are the increments of the local time of a Wiener process?
The local time L(x,t) at x of the Wiener process w is the length of time w spends at x before t. This has been the subject of extensive investigations. The main result of the authors may be stated as follows: Let \(a_ t\) be a non-decreasing function of t and suppose \(t^{-1}a_ t\) is non-increasing. Then \(\lim \sup_{t\to \infty}(L(t)-L(t-a_ t))/[a_ t(\log ta_ t^{-1}+2 \log \log t)]^{{1\over2}}=1.\)
big increments and continuity of Brownian local time
scientific article; zbMATH DE number 3868374