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The next meeting of the

National Seminar on Probability and Statistics

will be held on October 20, 2021 at 2:00 p.m. (UTC +3) in Zoom.

A talk on:

Brownian Motion Conditioned to Spend Limited Time Below a Barrier

will be delivered by

Dominic T. Schickentanz (Technical University of Darmstadt, Germany).

IMI BAS is inviting you to a scheduled Zoom meeting.

Topic: Национален семинар по стохастика
Time: Oct 20, 2021 14:00 Sofia
https://us02web.zoom.us/j/84710081103?pwd=Unl4aktJb2VpcWZQdEpDTDAzKysrQT09

Meeting ID: 847 1008 1103
Passcode: 925815

Abstract: We condition a Brownian motion with arbitrary starting point $y\in \mathbb{R}$ on spending at most $1$ time unit below $0$ and provide an explicit description of the resulting process. In particular, we provide explicit formulas for the distributions of its last zero $g=g^y$ and of its occupation time $\Gamma=\Gamma^y$ below $0$ as functions of $y$. This generalizes a result of Benjamini and Berestycki from 2011, which covers the special case $y=0$. Additionally, we study the behavior of the distributions of $g^y$ and $\Gamma^y$, respectively, for $y \to \pm\infty$. This is joint work with Frank Aurzada.