Infinite-horizon crossing probability for Brownian motion with negative drift

For

a, y > 0

,

P (sup_{u \geq 0} (W_{u} - a u) > y) = e^{- 2 a y} .

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Past exam of the mathematics course of the University of Cambridge / 2014 / iii / Paper 27 / 5 / c / 2 / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 203 / 2 / c / ii / Solution
Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 3 / 29K / d / Solution

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