Block records and maxima of the increments of the Wiener process
Let \(\{W(t), t\geq 0\}\), \(W(0)=0,\) be the Wiener process. The basic result of this paper consists in proving that there exists a r.v. \(N\) and a sequence \(\{Z_n \}\) of i.i.d. random variables such that a.s. for \(N\geq n\) the following equality is true \[ \max_{0\leq t\leq n}(W(t)-W(t+1))=\max(Z_1,\ldots ,Z_n). \]
scientific article; zbMATH DE number 1436935