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The tail of the maximum of Brownian motion minus a parabola
Brownian motion parabola
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2010/11/23
We give an asymptotic expression for the tail of the maximum of Brownian motion minus a parabola. This confirms a conjecture about the exponential term in the tail behavior, due to Svante Janson.
The maximum of Brownian motion minus a parabola
Brownian motion parabola
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2010/11/8
We derive a simple integral representation for the distribution of the maximum of Brownian motion minus a parabola, which can be used for computing the density and moments of the distribution, both fo...