Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-23T18:07:59.050Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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