Strong limit theorems for a simple random walk on the 2-dimensional comb.
On the joint distribution of the maximum and its location for a linear diffusion
Random walk local time approximated by a brownian sheet combined with an independent brownian motion
Let (, ) be the local time of a simple symmetric random walk on the line. We give a strong approximation of the centered local time process (, )−(0, ) in terms of a brownian sheet and an independent Wiener process (brownian motion), time changed by an independent brownian local time. Some related results and consequences are also established.
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