In this article we are mainly concerned with proving lower bounds on some uniform approximation schemes for the local times of one-dimensional Brownian motion. Consequently, this leads to many exact limit theorems for Brownian local times. The latter results are Paul Levy's occupation time approximation, the downcrossing theorem and an intrinsic construction.
Ann. Probab.
22(3):
1295-1330
(July, 1994).
DOI: 10.1214/aop/1176988604