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

Julien Randon-Furling, Paavo Salminen, Pierre Vallois

Research output: Contribution to journalArticleScientificpeer-review

1 Citation (Scopus)
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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 T m . The motivation for our work comes from a mathematical model for animal foraging. We also present results for Brownian motion with drift.

Original languageEnglish
Pages (from-to)1204-1221
Number of pages18
JournalStochastic Processes and their Applications
Volume150
DOIs
Publication statusPublished - Aug 2022
MoE publication typeA1 Journal article-refereed

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