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

DOI10.1016/J.SPA.2021.12.015zbMATH Open1491.60145arXiv2103.08358OpenAlexW3136737219WikidataQ114130751 ScholiaQ114130751MaRDI QIDQ2145826

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Publication date: 20 June 2022

Published in: (Search for Journal in Brave)

Abstract: Let $(S_t{)}_{tgeq0}$ be the running maximum of a standard Brownian motion $(B_t{)}_{tgeq0}$ and $T_m:=inft;,m{S}_t<t,,m>0$. 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.

Full work available at URL: https://arxiv.org/abs/2103.08358

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