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Distribution of the Supremum of the Two-Parameter Yeh-Wiener Process on the Boundary

S. R. Paranjape and C. Park
Journal of Applied Probability
Vol. 10, No. 4 (Dec., 1973), pp. 875-880
DOI: 10.2307/3212390
Stable URL: http://www.jstor.org/stable/3212390
Page Count: 6
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Distribution of the Supremum of the Two-Parameter Yeh-Wiener Process on the Boundary
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Abstract

Let D = [0,S]x[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.

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