Brownian Local Time Approximated by a Wiener Sheet

Abstract

Let $L(a,t)$ be the local time of a Wiener process. Our main result says that the process $L(a,t) - L(0,t)$ can be strongly approximated by a process obtained from a Wiener sheet $W(a,t)$ and a local time process $\hat{L}(0,t)$, independent of $W(\cdot,\cdot)$.