On a first hit distribution of the running maximum of Brownian motion
Résumé
Let (S t) t≥0 be the running maximum of a standard Brownian motion (B t) t≥0 and T m := inf{t; mS t < t}, m > 0. In this note we calculate the joint distribution of T m and B Tm. The motivation for our work comes from a mathematical model for animal foraging. We also present results for Brownian motion with drift.
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