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 language | English |
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Pages (from-to) | 1204-1221 |
Number of pages | 18 |
Journal | Stochastic Processes and their Applications |
Volume | 150 |
DOIs | |
Publication status | Published - Aug 2022 |
MoE publication type | A1 Journal article-refereed |