English

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 L2L_2-norm on a long time interval. The obtained limiting process is a non-stationary Ornstein-Uhlenbeck process.

Keywords

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

R2 v1 2026-06-28T13:57:28.974Z