On the increments of the local time of a Wiener sheet
The Wiener sheet W can be viewed as a continuous random function defined on the quadrant [0,\(\infty)\times [0,\infty)\). The local time \(\eta\) (u,A) at level u is a (random) measure of the level set \(\{s\in A:W(s)=u\}\). Detailed estimates are used to obtain information about \(\eta\) (u,A) when A is small. For example: suppose K is a compact subset of the open quadrant (0,\(\infty)\times (0,\infty)\). Let S(h) be the supremum of \(\eta\) (u,Q) for all u and all boxes Q in K of area h or less. Then it follows rapidly from Theorem 3 that \(S(h)=o(h^{3/4}(\log h^{-1})^ 3)\) as \(h\to 0\), with probability one.
scientific article; zbMATH DE number 3930066