Let W(t) be a standard Wiener process with local time L(x, t). It is well-known that, as stochastic processes, L(0, t) and supo [less-than-or-equals, slant] s [less-than-or-equals, slant] tW(s) have the same distribution (Lévy, 1939). Here we give a new derivation of the distribution of L(x, t...

Let L(a, t) be the local time of a Wiener process, and put . It is shown that if g(t)=t1/2(log t)-1(log log t)-1 and . A similar result is proved for random g(t) depending on the maximum of the Wiener process. These results settle a problem posed by Csörgo and Révész [7].