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Journal Articles Stochastic Processes and their Applications Year : 2022

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

Abstract

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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Dates and versions

hal-03170250 , version 1 (16-03-2021)

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Julien Randon-Furling, Paavo Salminen, Pierre Vallois. On a first hit distribution of the running maximum of Brownian motion. Stochastic Processes and their Applications, 2022, 150, ⟨10.1016/j.spa.2021.12.015⟩. ⟨hal-03170250⟩
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