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An excursion approach to maxima of the Brownian Bridge

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Mihael Perman (Institute for Mathematics, Physics, Mechanics, Ljubljana, Slovenia) Jon A. Wellner (University of Washington, Seattle)

Probability · Submitted 22 Apr 2009

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion.

how it is stated · asserted 0.98 read the record →

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arXiv ID0904.3473 (version 2)
Pith IDD5K4RMVF, Pith's permanent record of this paper and its review
CitationLjubljana, Mechanics, Mihael Perman (Institute for Mathematics, Physics, Seattle), Slovenia) Jon A. Wellner (University of Washington. "An excursion approach to maxima of the Brownian Bridge." arXiv:0904.3473 (2009). https://pith.science/paper/D5K4RMVF
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,539 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.59 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.34 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. Only the Poisson character of the excursion process will be used. Particular cases of calculations include the distributions of the Kolmogorov-Smirnov statistic, the Kuiper statistic, and the ratio of the maximum positive ordinate to the minumum negative ordinate.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. background 1.00 0.04 0.04 asserted 1.00
s1 In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. contribution 0.98 0.94 0.57 asserted 0.98
s2 Only the Poisson character of the excursion process will be used. method 0.83 0.48 0.06 asserted 1.00
s3 Particular cases of calculations include the distributions of the Kolmogorov-Smirnov statistic, the Kuiper statistic, and the ratio of the maximum positive ordinate to the minumum negative ordinate. result 0.75 0.79 0.11 asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Functionals of Brownian bridge arise as limiting distributions in nonparametric statistics. In this paper we will give a derivation of distributions of extrema of the Brownian bridge based on excursion theory for Brownian motion. Only the Poisson character of the excursion process will be used. Particular cases of calculations include the distributions of the Kolmogorov-Smirnov statistic, the Kuiper statistic, and the ratio of the maximum positive ordinate to the minumum negative ordinate.

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