Asymptotics of a boundary crossing probability of a Brownian bridge with general trend (Q1419395)

The present paper offers a large deviation type result for the boundary crossing probability in a signal plus noise model given by the Brownian bridge \(B_0\) on \((0,1).\) Let \(h : (0,1) \rightarrow \mathbb{R}\) be a function. Then the results can be used in a model \(\gamma h + B_0\) for testing whether a signal is present (\(\gamma > 0\)) or not (\( \gamma = 0\)). The paper contains formulas for the exponential decay of the error probability of second kind for weighted Kolmogorov-Smirnov tests as \(\gamma \rightarrow \infty\).