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Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region

Published online by Cambridge University Press:  14 July 2016

Arthur H. C. Chan
Arthur H. C. Chan*
Affiliation:
Carleton University
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Abstract

Let W (s, t), s, t ≧ 0, be the two-parameter Yeh–Wiener process defined on the first quadrant of the plane, that is, a Gaussian process with independent increments in both directions. In this paper, a lower bound for the distribution of the supremum of W (s, t) over a rectangular region [0, S]×[0, T], for S, T > 0, is given. An upper bound for the same was known earlier, while its exact distribution is still unknown.

Keywords

TWO-PARAMETER YEH-WIENER PROCESSSEPARABLE GAUSSIAN PROCESSINDEPENDENT INCREMENTSSUPREMUM OF A TWO-PARAMETER GAUSSIAN PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 4 , December 1975 , pp. 824 - 830
Copyright
Copyright © Applied Probability Trust 1975 

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References

[1] Doob, J. L. (1949) Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Statist. 20, 393–403.Google Scholar
[2] Paranjape, S. R. and Park, C. (1973) Distribution of the supremum of the two-parameter Yeh–Wiener process on the boundary. J. Appl. Prob. 10, 875–880.CrossRefGoogle Scholar
[3] Malmquist, S. (1954) On certain confidence contours for distribution functions. Ann. Math. Statist. 25, 523–533.Google Scholar