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

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

Randon-Furling, Julien; Salminen, Paavo; Vallois, Pierre

Stochastic processes and their applications, 08/2022, Volume: 150

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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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Randon-Furling, Julien | Salminen, Paavo | Vallois, Pierre

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