On the infimum of the local time of a Wiener process
Tóm tắt
Let {W(t), t≧0} be a standard Wiener process, and let L(x, t) be its jointly continuous local time. Define
$$T_r = inf\{ t \geqq 0;L(0,t \geqq r)\} .$$
The upper and lower class behaviour of inf L(y, T
r) is investigated, where the infimum is taken on an interval, which is an appropriately chosen function of r.
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