Random walk local time approximated by a Wiener sheet combined with an independent Brownian motion
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Let $ξ(k,n)$ be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process $ξ(k,n)-ξ(0,n)$ in terms of a Wiener sheet and an independent Wiener process, time changed by an independent Brownian local time. Some related results and consequences are also established.