Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion

摘要

Let $\xi(k,n)$ be the local time of a simple symmetric random walk on theline. We give a strong approximation of the centered local time process$\xi(k,n)-\xi(0,n)$ in terms of a Wiener sheet and an independent Wienerprocess, time changed by an independent Brownian local time. Some relatedresults and consequences are also established.