SOME LOWER BOUNDS FOR THE DISTRIBUTION OF THE SUPREMUM OF THE YEH-WIENER PROCESS OVER A RECTANGULAR REGION

Let W (s, t), s, t O0, be the two-parameter Yeh-Wiener process defined on the first quadrant of the plane, that is, a Gaussian process with independent increments in both directions. In this paper, a lower bound for the distribution of the supremum of W (s, t) over a rectangular region [0, S] x [0, T], for S, T > O, is given. An upper bound for the same was known earlier, while its