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On functionals of the adjusted range process

Published online by Cambridge University Press:  14 July 2016

G. Hooghiemstra
G. Hooghiemstra*
Affiliation:
Technological University of Delft
*
∗Postal address: Onderafdeling der Wiskunde, Technische Hogeschool Delft, Postbus 356, 2600 AJ Delft, Holland.
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Abstract

Using a well-known transformation that preserves Wiener measure a theorem is proved that enables one to derive in a non-computational manner distributions of simple functionals of the so-called adjusted range process.

Keywords

BROWNIAN MOTION

Information

Type
Short Communications
Information
Journal of Applied Probability , Volume 24 , Issue 1 , March 1987 , pp. 252 - 257
Copyright
Copyright © Applied Probability Trust 1987 

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Footnotes

Part of the research was done while the author was visiting the University of British Columbia. This visit was financially supported by the Niels Stensen Stichting, Amsterdam, The Netherlands, and the Natural Science and Engineering Research Council of Canada.

References

Doob, J. L. (1949) Heuristic aproach to the Kolmogorov–Smirnov theorems. Ann. Math. Statist. 20, 393–403.10.1214/aoms/1177729991Google Scholar
Feller, W. (1951) The asymptotic distribution of the range of sums of independent random variables. Ann. Math. Statist. 22, 427–432.Google Scholar
Freedman, D. (1971) Brownian Motion and Diffusion. Holden-Day, San Francisco.Google Scholar
Troutman, B. M. (1978) Reservoir storage with dependent, periodic net inputs. Water Resources Res. 14, 395–401.Google Scholar
Troutman, B. M. (1979) Some results in periodic autoregression. Biometrika 66, 219–228.Google Scholar
Troutman, B. M. (1983) Weak convergence of the adjusted range of cumulative sums of exchangeable random variables. J. Appl. Prob. 20, 297–304.10.2307/3213803Google Scholar