Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

Abstract

Let D = [0, S ] × [0, T ] be a rectangle in E 2 and X ( s, t ), ( s, t )∈ D , be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X ( s, t ) on the boundary of D by taking the limit of the probability distribution of the supremum of X ( s, t ) along certain paths as these paths approach the boundary of D . The probability distribution of the supremum of X ( s, t ) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X ( s, t ) on D , which is unknown.