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arXiv · 2103.08358

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

Julien Randon-Furling·Paavo Salminen·Pierre Vallois
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Abstract

Let $(S_t)_{t\geq 0}$ be the running maximum of a standard Brownian motion $(B_t)_{t\geq 0}$ and $T_m:=\inf\{t; \, mS_t 0$. In this note we calculate the joint distribution of $T_m$ and $B_{T_m}$. 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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Julien Randon-Furling, Paavo Salminen, Pierre Vallois. 2021-03-15. On a first hit distribution of the running maximum of Brownian motion. https://arxiv.org/abs/2103.08358

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