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- W2085394294 abstract "Our main intention is to describe the behavior of the (cumulative) distribution function of the random variable M 0,1 ≔ sup 0⩽s,t⩽1 W(s,t) near 0, where W denotes one-dimensional, two-parameter Brownian sheet. A remarkable result of Florit and Nualart asserts that M 0,1 has a smooth density function with respect to Lebesgue's measure (cf. Florit and Nualart, 1995 . Statist. Probab. Lett. 22, 25–31). Our estimates, in turn, seem to imply that the behavior of the density function of M 0,1 near 0 is quite exotic and, in particular, there is no clear-cut notion of a two-parameter reflection principle. We also consider the supremum of Brownian sheet over rectangles that are away from the origin. We apply our estimates to get an infinite-dimensional analogue of Hirsch's theorem for Brownian motion." @default.
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- W2085394294 date "2000-11-01" @default.
- W2085394294 modified "2023-09-28" @default.
- W2085394294 title "Boundary crossings and the distribution function of the maximum of Brownian sheet" @default.
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- W2085394294 doi "https://doi.org/10.1016/s0304-4149(00)00031-4" @default.
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