A functional equation technique for obtaining wiener process probabilities associated with theorems of Kolmogorov-Smirnov type
Published online by Cambridge University Press: 24 October 2008
Extract
1. Introduction. Since the first proofs by Kolmogorov (13) and Smirnov ((14), (15)) of their well-known results on the limit distribution of the deviations of the sample distribution function, many alternative proofs of these results have been given. For example, we may cite the various approaches of Feller (4), Doob (3), Kac (8), Gnedenko and Korolyuk(7), and Anderson and Darling (1). The approaches of (3), (8) and (1) rest on a probabilistic computation regarding the Wiener process, and are justified by the paper of Donsker (2) (see also (11)). Of all these approaches, only those of (8) and (1) can be extended to obtain the limit distributions of the ‘k–sample’ generalizations of the Kolmogorov-Smirnov statistics suggested in (9), and the author ((9), (10)) and Gihman(6) carried out such proofs.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 55 , Issue 4 , October 1959 , pp. 328 - 332
- Copyright
- Copyright © Cambridge Philosophical Society 1959
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