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Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

Published online by Cambridge University Press:  14 July 2016

S. R. Paranjape  and
C. Park
S. R. Paranjape
Affiliation:
Miami University, Oxford, Ohio
C. Park
Affiliation:
Miami University, Oxford, Ohio
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Abstract

Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.

Keywords

TWO PARAMETER YEH-WIENER PROCESSSUPREMUM ON THE BOUNDARYPROBABILITY DISTRIBUTION
Type
Short Communications
Information
Journal of Applied Probability , Volume 10 , Issue 4 , December 1973 , pp. 875 - 880
Copyright
Copyright © Applied Probability Trust 1973 

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References

[1] Doob, J. L. (1949) Heuristic approach to the Kolmogorov-Smirnov theorems. Ann. Math. Statist. 20, 393–403.CrossRefGoogle Scholar
[2] Gikhman, I. I. and Skorokhod, A. V. (1969) Introduction to the Theory of Random Processes. W. B. Saunders, Philadelphia, London, Toronto.Google Scholar
[3] Malmquist, S. (1954) On certain confidence contours for distribution functions. Ann. Math. Statist. 25, 523–533.CrossRefGoogle Scholar
[4] Yeh, J. (1960) Wiener measure in a space of functions of two variables. Trans. Amer. Math. Soc. 95, 433–450.CrossRefGoogle Scholar