Brownian motion conditioned to have restricted $L_2$-norm
Probability
2024-09-04 v2
Abstract
We condition a Brownian motion on having an atypically small -norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.
Cite
@article{arxiv.2312.12982,
title = {Brownian motion conditioned to have restricted $L_2$-norm},
author = {Frank Aurzada and Mikhail Lifshits and Dominic T. Schickentanz},
journal= {arXiv preprint arXiv:2312.12982},
year = {2024}
}
Comments
16 pages