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Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region. J Appl Probab 2016. [DOI: 10.1017/s0021900200048798] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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.
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Klesov OI, Kruglova NV. The distribution of a functional of the Wiener process and its application to the Brownian sheet. STATISTICS-ABINGDON 2011. [DOI: 10.1080/02331888.2010.541251] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Abrahams J. Distribution of the supremum of the two-parameter slepian process on the boundary of the unit square. Stoch Process Their Appl 1984. [DOI: 10.1016/0304-4149(84)90171-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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