## An excursion approach to maxima of the Brownian bridge.(English)Zbl 1306.60115

Summary: Distributions of functionals of the Brownian bridge arise as limiting distributions in non-parametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. The idea of rescaling and conditioning on the local time has been used widely in the literature. In this paper it is used to give a unified derivation of a number of known distributions, and a few new ones. Particular cases of calculations include the distribution of the Kolmogorov-Smirnov statistic and the Kuiper statistic.

### MSC:

 60J65 Brownian motion 60G55 Point processes (e.g., Poisson, Cox, Hawkes processes) 60J55 Local time and additive functionals 62E20 Asymptotic distribution theory in statistics
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### References:

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