论文信息 - On a first hit distribution of the running maximum of Brownian motion

On a first hit distribution of the running maximum of Brownian motion

Let (St)t≥0 be the running maximum of a standard Brownian motion (Bt)t≥0 and Tm := inf{t; mSt < t}, m > 0. In this note we calculate the joint distribution of Tm and BTm . 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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