Geodesic
On~the limit distribution of Kolmogorov--Smirnov statistics for a~composite hypothesis
Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 619-646.

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By differential equation methods the author finds a complete asymptotic expansion for the probability of overshooting a high level of a conditional Wiener process given on an interval. These results are used to compute approximate values of percentage points for Kolmogorov–Smirnov statistics in the case of a composite hypothesis. A comparison between the results thus calculated and tabular values is carried out for a number of distributions. Bibliography: 19 titles. 
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Yu. N. Tyurin. On~the limit distribution of Kolmogorov--Smirnov statistics for a~composite hypothesis. Izvestiya. Mathematics , Tome 25 (1985) no. 3, pp. 619-646. http://geodesic.mathdoc.fr/item/IM2_1985_25_3_a10/

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