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

Julien Randon-Furling, Paavo Salminen and Pierre Vallois

Stochastic Processes and their Applications, 2022, vol. 150, issue C, 1204-1221

Abstract: Let (St)t≥0 be the running maximum of a standard Brownian motion (Bt)t≥0 and Tm≔inf{t;mSt0. In this note we calculate the joint distribution of Tm and BTm. The motivation for our work comes from a mathematical model for animal foraging. We also present results for Brownian motion with drift.

Keywords: Subordinator; Spectrally negative Lévy process; Excursion; Integral equation; Path transformation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2021.12.015

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