We show a lower bound for the boundary crossing probability P{[there exists]z[set membership, variant][0,1]:h(z)+B0(z)u(z)} with B0 a Brownian bridge, h a trend function and u a boundary function. By that we get also a lower bound for the boundary crossing probability P{[there exists]z[set...

Given a Brownian bridge B0 with trend g:[0,1]--[0,[infinity]), Y(z)=g(z)+B0(z),z[set membership, variant][0,1],we are interested in testing H0:g[reverse not equivalent]0 against the alternative K:g0. For this test problem we study weighted Kolmogorov testswhere c0 is a suitable constant and...