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We derive asymptotic behavior of the probability of high-level excursion for the maximal increment of the Wiener process.

statistics extreme extremes value process theory asymptotics large wiener large-deviations deviations shepp-statistics wiener-process increments high-level-excursions shepp

We derive asymptotic behavior of the probability of high-level excursion for the maximal increment of a Gaussian random walk.

statistics extreme random extremes value gaussian theory asymptotics walk large large-deviations deviations shepp-statistics increments high-level-excursions gaussian-random-walk shepp

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