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

التفاصيل البيبلوغرافية
العنوان: On a first hit distribution of the running maximum of Brownian motion
المؤلفون: Randon-Furling, Julien, Salminen, Paavo, Vallois, Pierre
سنة النشر: 2021
المجموعة: Mathematics
Condensed Matter
مصطلحات موضوعية: Mathematics - Probability, Condensed Matter - Statistical Mechanics, 60J65, 60G17, 60G40, 60G51, 60G52
الوصف: Let $(S_t)_{t\geq 0}$ be the running maximum of a standard Brownian motion $(B_t)_{t\geq 0}$ and $T_m:=\inf\{t; \, mS_t0$. 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.
Comment: 24 pages, 2 figures, submitted
نوع الوثيقة: Working Paper
URL الوصول: http://arxiv.org/abs/2103.08358
رقم الأكسشن: edsarx.2103.08358
قاعدة البيانات: arXiv