Rate of escape of conditioned Brownian motion

Orphée Collin (1) , Francis Comets (2)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation

We study the norm of the two-dimensional Brownian motion conditioned to stay outside the unit disk at all times. We obtain sharp results on the rate of escape to infinity of the process of future minima. For this, we introduce a renewal structure attached to record times and values. Additional results are given for the long time behavior of the norm.

Mots clés: upper-class and lower-class; regeneration; Wiener moustache; transience; conditioning; Bessel process; Brownian motion; random difference equation; random difference equation AMS 2020 subject classifications: 60K35; 60J60; 60J65; 60G17

Domaines: Mathématiques [math]

Orphée Collin, Francis Comets. Rate of escape of conditioned Brownian motion. 2021. ⟨hal-03146283v2⟩